1 00:00:00,135 --> 00:00:02,490 The following content is provided under a Creative 2 00:00:02,490 --> 00:00:04,030 Commons license. 3 00:00:04,030 --> 00:00:06,330 Your support will help MIT OpenCourseWare 4 00:00:06,330 --> 00:00:10,690 continue to offer high quality educational resources for free. 5 00:00:10,690 --> 00:00:13,320 To make a donation or view additional materials 6 00:00:13,320 --> 00:00:17,280 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:17,280 --> 00:00:18,430 at ocw.mit.edu. 8 00:00:26,458 --> 00:00:27,422 VINA NGUYEN: Hi. 9 00:00:27,422 --> 00:00:28,901 Are you guys all ready? 10 00:00:28,901 --> 00:00:29,400 All set? 11 00:00:29,400 --> 00:00:30,730 OK. 12 00:00:30,730 --> 00:00:33,400 So my name is Vina Nguyen. 13 00:00:33,400 --> 00:00:36,370 I'm at MIT, going to be a senior next year. 14 00:00:36,370 --> 00:00:38,920 I'm studying electrical engineering and computer 15 00:00:38,920 --> 00:00:39,770 science. 16 00:00:39,770 --> 00:00:41,020 That's just one major-- 17 00:00:41,020 --> 00:00:43,480 half of both. 18 00:00:43,480 --> 00:00:45,250 And I'm teaching probability because I 19 00:00:45,250 --> 00:00:50,432 thought it was an intro class that I really liked a lot. 20 00:00:50,432 --> 00:00:51,388 OK, hold on. 21 00:00:58,080 --> 00:00:59,040 [DOOR CLOSING] 22 00:00:59,040 --> 00:00:59,720 Yeah. 23 00:00:59,720 --> 00:01:00,610 Sorry. 24 00:01:00,610 --> 00:01:04,190 I speak kind of soft, so if you can't hear me, just tell me, 25 00:01:04,190 --> 00:01:05,540 and I'll try to speak louder. 26 00:01:08,340 --> 00:01:10,150 OK. 27 00:01:10,150 --> 00:01:14,040 So there's a few announcements I have to go over. 28 00:01:14,040 --> 00:01:16,620 First, you need to be here because you 29 00:01:16,620 --> 00:01:19,480 want to be here, not because your parents want to be here. 30 00:01:19,480 --> 00:01:22,320 So if you want to leave, leave. 31 00:01:22,320 --> 00:01:25,470 But I want you to take it because you want to take it. 32 00:01:25,470 --> 00:01:28,710 That's the best way to learn. 33 00:01:28,710 --> 00:01:30,861 During registration you also got your sheet 34 00:01:30,861 --> 00:01:31,860 with the blank schedule. 35 00:01:31,860 --> 00:01:33,120 I gave you that sticker. 36 00:01:33,120 --> 00:01:34,514 So you can put it on there. 37 00:01:34,514 --> 00:01:35,430 And everyone did that? 38 00:01:35,430 --> 00:01:36,810 OK. 39 00:01:36,810 --> 00:01:39,810 So next week, you should come to this room directly. 40 00:01:39,810 --> 00:01:42,710 So don't come to Lobby 13. 41 00:01:42,710 --> 00:01:43,740 Just come directly here. 42 00:01:48,970 --> 00:01:49,470 OK. 43 00:01:49,470 --> 00:01:51,360 So on your registration sheet, they also 44 00:01:51,360 --> 00:01:55,680 told you about a server called Caroline. 45 00:01:55,680 --> 00:01:57,330 So for my class, on the sticker you 46 00:01:57,330 --> 00:02:01,490 need to type in the password, which is frog something. 47 00:02:01,490 --> 00:02:03,830 And I'm going to post these slides up there, 48 00:02:03,830 --> 00:02:07,170 or any lecture notes I had in case you missed a class, 49 00:02:07,170 --> 00:02:10,590 or you wanted to review something. 50 00:02:10,590 --> 00:02:14,700 There is chat and forums, but I work full time during the week. 51 00:02:14,700 --> 00:02:18,240 So I probably won't have time to always chat with you guys. 52 00:02:18,240 --> 00:02:20,850 But my email is listed on the syllabus 53 00:02:20,850 --> 00:02:23,830 if you do have questions. 54 00:02:23,830 --> 00:02:25,830 I always check my email, but I don't necessarily 55 00:02:25,830 --> 00:02:26,580 have time to chat. 56 00:02:26,580 --> 00:02:33,024 So email is good if you have questions. 57 00:02:33,024 --> 00:02:35,440 Fourth announcement, there is a lunch-time activities form 58 00:02:35,440 --> 00:02:35,981 you also got. 59 00:02:35,981 --> 00:02:39,010 You need to get that signed. 60 00:02:39,010 --> 00:02:40,960 Make sure you turn it in next week, 61 00:02:40,960 --> 00:02:46,760 because HSSP won't take it the week after next week. 62 00:02:46,760 --> 00:02:48,460 And if you have any other questions 63 00:02:48,460 --> 00:02:52,210 about administrative stuff, go to the HSSP office, 64 00:02:52,210 --> 00:02:54,590 because I'm just a teacher here to teach and not 65 00:02:54,590 --> 00:02:56,760 here to manage paperwork. 66 00:02:56,760 --> 00:02:57,280 OK. 67 00:02:57,280 --> 00:03:03,620 So now that that's done, I'm going to start. 68 00:03:03,620 --> 00:03:06,050 OK. 69 00:03:06,050 --> 00:03:08,000 So as you all know, this is probability. 70 00:03:08,000 --> 00:03:10,280 I told you a little bit about myself, 71 00:03:10,280 --> 00:03:14,600 but I also want to know a little bit about you guys. 72 00:03:14,600 --> 00:03:16,600 I have never been to Boston except for college, 73 00:03:16,600 --> 00:03:18,890 so I'm not entirely sure what it's like. 74 00:03:18,890 --> 00:03:20,930 If you could go around and tell me 75 00:03:20,930 --> 00:03:26,060 your name, and what grade you are, and what school, then-- 76 00:03:26,060 --> 00:03:27,800 start with you. 77 00:03:27,800 --> 00:03:29,300 AUDIENCE: I'm Margaret [INAUDIBLE].. 78 00:03:29,300 --> 00:03:32,410 I'm going to ninth grade, and I'm 79 00:03:32,410 --> 00:03:35,725 going to [INAUDIBLE] High School. 80 00:03:35,725 --> 00:03:38,210 VINA NGUYEN: OK. 81 00:03:38,210 --> 00:03:40,695 That way. 82 00:03:40,695 --> 00:03:42,200 AUDIENCE: [INAUDIBLE]. 83 00:03:42,200 --> 00:03:47,329 And I'm going to junior year. 84 00:03:47,329 --> 00:03:49,784 And to Wellesley. 85 00:03:49,784 --> 00:03:50,970 AUDIENCE: My name is Iris. 86 00:03:50,970 --> 00:03:53,172 And I'm also going to Wellesley. 87 00:03:53,172 --> 00:03:56,127 And I'm going to be in 12th grade. 88 00:03:56,127 --> 00:03:57,210 AUDIENCE: I'm [INAUDIBLE]. 89 00:03:57,210 --> 00:03:58,460 I'm going to be in 12th grade. 90 00:03:58,460 --> 00:04:00,090 I'm related to her. 91 00:04:00,090 --> 00:04:03,742 And yeah, so I go to Wellesley. 92 00:04:03,742 --> 00:04:06,540 AUDIENCE: I'm Amy, And I'm going to ninth grade 93 00:04:06,540 --> 00:04:07,647 at Wellesley High School. 94 00:04:07,647 --> 00:04:08,188 AUDIENCE: Hi. 95 00:04:08,188 --> 00:04:12,134 I'm [INAUDIBLE],, and I'm going to be a junior at [INAUDIBLE] 96 00:04:12,134 --> 00:04:12,634 High School. 97 00:04:12,634 --> 00:04:16,092 AUDIENCE: I'm [INAUDIBLE],, and I'm going to be in ninth grade, 98 00:04:16,092 --> 00:04:18,068 and I go to [INAUDIBLE] Middle School. 99 00:04:18,068 --> 00:04:21,360 AUDIENCE: I'm [INAUDIBLE],, and I'm going to eighth grade, 100 00:04:21,360 --> 00:04:25,020 also, in Stonybrook. 101 00:04:25,020 --> 00:04:27,890 AUDIENCE: My name's Kevin, and I'm going to seventh grade. 102 00:04:27,890 --> 00:04:31,850 And I'm going to Boston Latin Academy next year. 103 00:04:31,850 --> 00:04:36,305 AUDIENCE: I'm Diana, and I'm going to junior year also. 104 00:04:36,305 --> 00:04:41,255 And I'm going to [INAUDIBLE] High School. 105 00:04:41,255 --> 00:04:42,245 AUDIENCE: I'm Andrew. 106 00:04:42,245 --> 00:04:44,225 I'm going into seventh grade. 107 00:04:44,225 --> 00:04:45,710 I'm going to Cherry Hill. 108 00:04:45,710 --> 00:04:46,710 AUDIENCE: I'm Ben. 109 00:04:46,710 --> 00:04:51,955 I'm going into sophomore year at Kingsbury Oxford. 110 00:04:51,955 --> 00:04:55,183 AUDIENCE: I'm Pierre, and I'm going to 11th grade 111 00:04:55,183 --> 00:04:56,656 at [INAUDIBLE]. 112 00:04:56,656 --> 00:04:57,638 AUDIENCE: I'm Tina. 113 00:04:57,638 --> 00:05:00,534 I'm going to be a junior at [INAUDIBLE] High. 114 00:05:00,534 --> 00:05:01,075 AUDIENCE: Me? 115 00:05:01,075 --> 00:05:01,956 VINA NGUYEN: Yeah. 116 00:05:01,956 --> 00:05:03,039 AUDIENCE: I'm [INAUDIBLE]. 117 00:05:03,039 --> 00:05:06,967 I'm going to seventh grade, And I'm going with Wellesley Middle 118 00:05:06,967 --> 00:05:07,876 School. 119 00:05:07,876 --> 00:05:09,750 AUDIENCE: I'm Alan I'm going to eighth grade, 120 00:05:09,750 --> 00:05:12,300 and I'm going to Boston Latin School. 121 00:05:12,300 --> 00:05:13,533 AUDIENCE: I'm James. 122 00:05:13,533 --> 00:05:17,160 I'm going to eighth grade, and I go to [INAUDIBLE] School. 123 00:05:17,160 --> 00:05:19,830 VINA NGUYEN: OK So I guess we have a pretty good range. 124 00:05:22,982 --> 00:05:23,710 Shh. 125 00:05:23,710 --> 00:05:25,660 Thank you. 126 00:05:25,660 --> 00:05:28,570 So I'm sure you guys know this is all for beginners. 127 00:05:28,570 --> 00:05:33,350 If you already know this stuff, you have no reason to be here. 128 00:05:33,350 --> 00:05:36,150 This lecture, I'm probably going to use mostly PowerPoint. 129 00:05:36,150 --> 00:05:38,760 If I do some things, I'll use the chalkboard. 130 00:05:38,760 --> 00:05:41,440 And we'll work out problems, either as a class, 131 00:05:41,440 --> 00:05:42,420 or I'll hand out stuff. 132 00:05:42,420 --> 00:05:44,210 And there is no homework. 133 00:05:44,210 --> 00:05:47,700 So and please feel free to ask questions. 134 00:05:47,700 --> 00:05:49,950 I don't want to move on unless you guys understand it. 135 00:05:49,950 --> 00:05:50,880 It's like math. 136 00:05:50,880 --> 00:05:53,940 Everything later builds up on what you knew before. 137 00:05:57,730 --> 00:05:58,360 OK. 138 00:05:58,360 --> 00:06:01,690 So why should we study probability? 139 00:06:01,690 --> 00:06:05,200 Well first, you want to model the uncertain. 140 00:06:05,200 --> 00:06:08,606 It's easy to be like, oh, I don't know anything about this, 141 00:06:08,606 --> 00:06:09,730 so I can't decide anything. 142 00:06:09,730 --> 00:06:10,900 I can't estimate anything. 143 00:06:10,900 --> 00:06:13,090 But with probability, you can at least 144 00:06:13,090 --> 00:06:16,230 get a sense of what's going on with the world. 145 00:06:16,230 --> 00:06:19,330 And it's not just that you want to know what's going on, 146 00:06:19,330 --> 00:06:22,830 but you also want to decide based on it. 147 00:06:22,830 --> 00:06:25,540 And then for the third point especially, there's 148 00:06:25,540 --> 00:06:27,490 also studies out there in the news, 149 00:06:27,490 --> 00:06:29,200 they make up some random statistic-- 150 00:06:29,200 --> 00:06:32,196 I mean, not always, but it could sound that way-- 151 00:06:32,196 --> 00:06:33,820 but if you have probability background, 152 00:06:33,820 --> 00:06:37,450 you can at least take a more intellectual approach to it. 153 00:06:37,450 --> 00:06:40,120 You can't just take it as is. 154 00:06:40,120 --> 00:06:42,250 You need to question other factors, 155 00:06:42,250 --> 00:06:45,190 or maybe there's a certain way of sampling 156 00:06:45,190 --> 00:06:46,580 that they did wrong. 157 00:06:46,580 --> 00:06:48,760 So this would help you to understand 158 00:06:48,760 --> 00:06:55,240 more what the studies are confirming or suggesting. 159 00:06:55,240 --> 00:06:58,960 Some examples are like, what's the weather like tomorrow, sun, 160 00:06:58,960 --> 00:07:00,850 rain, how much percent? 161 00:07:00,850 --> 00:07:03,130 What are the chances of a drug working-- 162 00:07:03,130 --> 00:07:07,370 depending on the factors of the person, their age, 163 00:07:07,370 --> 00:07:09,610 their gender, their medical background-- 164 00:07:09,610 --> 00:07:12,730 how successful will this drug be? 165 00:07:12,730 --> 00:07:16,230 Third kind, what kind of customer will buy my product? 166 00:07:16,230 --> 00:07:20,230 Maybe based on their buying behavior or their demographics, 167 00:07:20,230 --> 00:07:22,180 how likely will this product sell to them? 168 00:07:22,180 --> 00:07:24,280 How profitable will it be? 169 00:07:24,280 --> 00:07:26,240 Fourth one, should I buy a lottery ticket? 170 00:07:26,240 --> 00:07:27,575 Will two help? 171 00:07:27,575 --> 00:07:29,200 And then there's also bio-applications, 172 00:07:29,200 --> 00:07:32,150 like whether your child will be a boy or a girl. 173 00:07:32,150 --> 00:07:35,320 Hopefully you guys aren't there yet. 174 00:07:35,320 --> 00:07:38,310 So now you know why we should learn probability, 175 00:07:38,310 --> 00:07:40,870 you should know there's two actually 176 00:07:40,870 --> 00:07:43,300 different definitions for it. 177 00:07:43,300 --> 00:07:46,820 The first one is frequency probability, 178 00:07:46,820 --> 00:07:48,070 which is the more physical. 179 00:07:48,070 --> 00:07:51,310 Like, if you repeat something over and over again, 180 00:07:51,310 --> 00:07:55,360 how often will the result happen? 181 00:07:55,360 --> 00:07:58,000 So how likely is a certain event that you 182 00:07:58,000 --> 00:08:02,320 know is the same every time going to happen? 183 00:08:02,320 --> 00:08:04,420 And the second one is Bayesian probability, 184 00:08:04,420 --> 00:08:07,000 which we will get to later, and that's 185 00:08:07,000 --> 00:08:14,140 a measure more of how sure you are that something will happen 186 00:08:14,140 --> 00:08:15,310 given the evidence. 187 00:08:20,780 --> 00:08:25,160 So in Bayesian probability, unlike frequency probability, 188 00:08:25,160 --> 00:08:28,610 you can't repeat something over and over again. 189 00:08:28,610 --> 00:08:31,040 An example of that would be like, 190 00:08:31,040 --> 00:08:33,409 how likely am I going to get an A given 191 00:08:33,409 --> 00:08:37,820 that I attended all the classes, or I participated, 192 00:08:37,820 --> 00:08:40,770 or that-- you can't repeat that experiment over and over again. 193 00:08:40,770 --> 00:08:43,740 It's a measure of belief. 194 00:08:43,740 --> 00:08:45,920 So is that clear to everyone? 195 00:08:45,920 --> 00:08:47,870 OK. 196 00:08:47,870 --> 00:08:50,840 So we're going to look at frequency probability 197 00:08:50,840 --> 00:08:52,290 a little bit more. 198 00:08:52,290 --> 00:08:56,030 I'm sure you guys know that there's a 50% chance 199 00:08:56,030 --> 00:08:57,106 that heads will come up-- 200 00:08:57,106 --> 00:08:58,980 or tails will come up-- when you flip a coin. 201 00:08:58,980 --> 00:09:02,150 But how exactly are you going to measure that? 202 00:09:02,150 --> 00:09:04,766 I mean, you could flip it once, or you could flip it twice, 203 00:09:04,766 --> 00:09:06,140 or you could flip it three times, 204 00:09:06,140 --> 00:09:08,600 or you could flip it a lot of times 205 00:09:08,600 --> 00:09:11,210 and then figure out the ratio of heads to tails. 206 00:09:15,770 --> 00:09:20,790 So we're going to do not necessarily an experiment. 207 00:09:20,790 --> 00:09:23,810 I have a coin, and we're going to flip 208 00:09:23,810 --> 00:09:26,720 it a large number of times. 209 00:09:26,720 --> 00:09:29,450 And I want you to observe the percent of heads 210 00:09:29,450 --> 00:09:30,980 that comes up after each time. 211 00:09:30,980 --> 00:09:33,590 So you want to take the average of heads 212 00:09:33,590 --> 00:09:37,520 that comes out after one time, after two times, 213 00:09:37,520 --> 00:09:40,160 after 10 times, et cetera. 214 00:09:40,160 --> 00:09:43,740 And what I want you to do is observe what happens initially, 215 00:09:43,740 --> 00:09:46,220 so after one or three times, and then 216 00:09:46,220 --> 00:09:48,350 what happens after a while. 217 00:09:48,350 --> 00:09:56,960 So what I actually have here is an Excel sheet. 218 00:09:56,960 --> 00:09:59,080 If you can see on the left column, 219 00:09:59,080 --> 00:10:01,090 it's the number of trials. 220 00:10:01,090 --> 00:10:06,670 The second one is a 1 or 0, 1 being heads and 0 being tails. 221 00:10:06,670 --> 00:10:11,240 And then after each time, it calculates the ratio of heads. 222 00:10:11,240 --> 00:10:15,205 So the way we graph this-- 223 00:10:21,230 --> 00:10:22,751 can everyone see this? 224 00:10:22,751 --> 00:10:23,250 Yeah. 225 00:10:23,250 --> 00:10:25,660 OK. 226 00:10:25,660 --> 00:10:29,760 So you know a probability goes from 0 to 100. 227 00:10:29,760 --> 00:10:36,570 So that would be 0% heads and then 100%. 228 00:10:36,570 --> 00:10:40,260 And you're expecting around 50%, right? 229 00:10:40,260 --> 00:10:47,000 So that's 50, 10, 20, 30, 40, 60, 70. 230 00:10:47,000 --> 00:10:47,500 OK. 231 00:10:47,500 --> 00:10:49,320 And then your x-axis is the number 232 00:10:49,320 --> 00:10:55,290 of trials, so the number of times you flip your coin. 233 00:10:55,290 --> 00:10:58,000 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. 234 00:10:58,000 --> 00:11:03,940 OK, we have around 15 people, but probably go up to 20 times. 235 00:11:08,462 --> 00:11:10,810 OK. 236 00:11:10,810 --> 00:11:14,080 So I have a coin, and I want each of you 237 00:11:14,080 --> 00:11:17,340 to flip it and tell me if it comes up heads or tails. 238 00:11:17,340 --> 00:11:20,463 And then I'll use the Excel chart to calculate it. 239 00:11:20,463 --> 00:11:20,963 OK. 240 00:11:24,400 --> 00:11:26,855 [COIN LANDING] 241 00:11:26,855 --> 00:11:27,837 AUDIENCE: Heads. 242 00:11:27,837 --> 00:11:29,800 VINA NGUYEN: Heads. 243 00:11:29,800 --> 00:11:30,300 OK. 244 00:11:30,300 --> 00:11:39,297 So right now, your ratio is 100% because one out of one heads. 245 00:11:39,297 --> 00:11:40,880 Give it to the next person behind you. 246 00:11:46,210 --> 00:11:47,130 AUDIENCE: Tails. 247 00:11:47,130 --> 00:11:49,490 VINA NGUYEN: Tails? 248 00:11:49,490 --> 00:11:51,320 OK, so 50%. 249 00:11:51,320 --> 00:11:51,820 Next person. 250 00:11:57,688 --> 00:11:58,666 AUDIENCE: Tails. 251 00:11:58,666 --> 00:12:00,130 VINA NGUYEN: Tails. 252 00:12:00,130 --> 00:12:00,630 OK. 253 00:12:00,630 --> 00:12:06,889 So now you're at 33%, just like around here. 254 00:12:06,889 --> 00:12:07,555 AUDIENCE: Tails. 255 00:12:10,392 --> 00:12:11,100 VINA NGUYEN: 25%. 256 00:12:14,628 --> 00:12:16,800 [COIN LANDING] 257 00:12:16,800 --> 00:12:17,466 AUDIENCE: Heads. 258 00:12:17,466 --> 00:12:19,131 VINA NGUYEN: Heads. 259 00:12:19,131 --> 00:12:19,630 40%. 260 00:12:23,824 --> 00:12:24,899 AUDIENCE: Tails. 261 00:12:24,899 --> 00:12:25,690 VINA NGUYEN: Tails. 262 00:12:25,690 --> 00:12:27,370 It's 33%. 263 00:12:31,298 --> 00:12:32,471 AUDIENCE: Tails. 264 00:12:32,471 --> 00:12:33,262 VINA NGUYEN: Tails. 265 00:12:38,070 --> 00:12:38,570 29%. 266 00:12:41,243 --> 00:12:41,909 AUDIENCE: Tails. 267 00:12:44,482 --> 00:12:45,190 VINA NGUYEN: 25%. 268 00:12:49,348 --> 00:12:50,280 AUDIENCE: Heads. 269 00:12:50,280 --> 00:12:52,710 VINA NGUYEN: Heads. 270 00:12:52,710 --> 00:12:54,594 33%. 271 00:12:54,594 --> 00:12:56,546 [COIN LANDING] 272 00:12:56,546 --> 00:12:59,012 AUDIENCE: Tails. 273 00:12:59,012 --> 00:12:59,720 VINA NGUYEN: 30%. 274 00:13:04,360 --> 00:13:05,054 AUDIENCE: Tails. 275 00:13:05,054 --> 00:13:05,845 VINA NGUYEN: Tails. 276 00:13:08,671 --> 00:13:09,170 27%. 277 00:13:11,910 --> 00:13:12,870 AUDIENCE: Heads. 278 00:13:12,870 --> 00:13:13,661 VINA NGUYEN: Heads. 279 00:13:20,070 --> 00:13:21,980 33%. 280 00:13:21,980 --> 00:13:23,650 Was that the last person? 281 00:13:23,650 --> 00:13:24,530 OK. 282 00:13:24,530 --> 00:13:25,440 Oh, go around. 283 00:13:25,440 --> 00:13:26,601 OK. 284 00:13:26,601 --> 00:13:27,226 AUDIENCE: Yeah. 285 00:13:27,226 --> 00:13:29,686 We've got to go too. 286 00:13:29,686 --> 00:13:30,371 AUDIENCE: Tails. 287 00:13:30,371 --> 00:13:31,162 VINA NGUYEN: Tails. 288 00:13:34,106 --> 00:13:34,606 31%. 289 00:13:39,034 --> 00:13:40,018 AUDIENCE: Heads. 290 00:13:40,018 --> 00:13:41,324 VINA NGUYEN: Heads? 291 00:13:41,324 --> 00:13:41,990 AUDIENCE: Tails. 292 00:13:41,990 --> 00:13:42,698 VINA NGUYEN: 36%. 293 00:13:50,715 --> 00:13:51,693 AUDIENCE: Heads. 294 00:13:51,693 --> 00:13:54,630 VINA NGUYEN: Heads. 295 00:13:54,630 --> 00:13:55,471 40%. 296 00:13:55,471 --> 00:13:57,880 OK. 297 00:13:57,880 --> 00:14:04,925 So oh, not done yet. 298 00:14:04,925 --> 00:14:05,758 AUDIENCE: Of course. 299 00:14:09,662 --> 00:14:10,948 AUDIENCE: Heads. 300 00:14:10,948 --> 00:14:11,614 AUDIENCE: Heads. 301 00:14:15,672 --> 00:14:16,380 VINA NGUYEN: 44%. 302 00:14:24,045 --> 00:14:25,020 AUDIENCE: Tails. 303 00:14:25,020 --> 00:14:27,570 VINA NGUYEN: Tails. 304 00:14:27,570 --> 00:14:29,060 AUDIENCE: Anybody else? 305 00:14:29,060 --> 00:14:30,128 VINA NGUYEN: Anyone else? 306 00:14:30,128 --> 00:14:31,960 No. 307 00:14:31,960 --> 00:14:32,876 AUDIENCE: No. 308 00:14:32,876 --> 00:14:34,671 VINA NGUYEN: Thank you. 309 00:14:34,671 --> 00:14:35,170 OK. 310 00:14:35,170 --> 00:14:39,130 So you have a pretty small group. 311 00:14:39,130 --> 00:14:40,900 If you were to take just that experiment, 312 00:14:40,900 --> 00:14:44,770 you would assume that heads showed up about 40% 313 00:14:44,770 --> 00:14:45,910 of the time. 314 00:14:45,910 --> 00:14:47,240 That's not true, right? 315 00:14:47,240 --> 00:14:52,280 So you need to have a larger sample. 316 00:14:52,280 --> 00:14:59,860 So in this one, you guys can see that I auto-generated 317 00:14:59,860 --> 00:15:04,120 the same experiment, but 500 times, which we can't do today. 318 00:15:04,120 --> 00:15:07,370 It'd take way too long. 319 00:15:07,370 --> 00:15:09,730 But if you can see at the beginning, which 320 00:15:09,730 --> 00:15:14,740 is kind of what we did, it varies a lot. 321 00:15:14,740 --> 00:15:17,740 The 20 here would be like this part, 322 00:15:17,740 --> 00:15:19,870 where it's still very variable. 323 00:15:19,870 --> 00:15:22,360 But after a very long number of times, 324 00:15:22,360 --> 00:15:26,360 it will eventually converge to 50%. 325 00:15:26,360 --> 00:15:32,710 So this is actually the law of large numbers-- 326 00:15:32,710 --> 00:15:35,700 the explanation for that we can cover later-- 327 00:15:35,700 --> 00:15:39,050 but this is just an example of how you would figure out what 328 00:15:39,050 --> 00:15:40,510 a frequency probability is. 329 00:15:40,510 --> 00:15:44,180 And you need to know how many times you need to do that. 330 00:15:44,180 --> 00:15:48,940 So this law is only relevant for large numbers, 331 00:15:48,940 --> 00:15:50,160 hence, large number. 332 00:15:54,110 --> 00:15:56,350 So does that make sense to everyone? 333 00:15:56,350 --> 00:15:56,850 OK. 334 00:16:04,820 --> 00:16:10,220 Before we do probability, one of the very important things 335 00:16:10,220 --> 00:16:12,200 is set theory. 336 00:16:12,200 --> 00:16:15,120 I can't remember if high school taught you guys that. 337 00:16:15,120 --> 00:16:18,800 Do you guys know what set theory is, just a little bit basic 338 00:16:18,800 --> 00:16:19,850 understanding? 339 00:16:19,850 --> 00:16:20,910 OK. 340 00:16:20,910 --> 00:16:23,840 I'm just going to go through it just in case for you guys 341 00:16:23,840 --> 00:16:27,410 who need the refresher. 342 00:16:27,410 --> 00:16:31,132 So a set is a collection of objects. 343 00:16:31,132 --> 00:16:32,840 For example, there's outcomes of the die. 344 00:16:32,840 --> 00:16:38,030 You can have 1, 2, 3, all the way to 6. 345 00:16:38,030 --> 00:16:40,130 And each object in a set is called an element. 346 00:16:40,130 --> 00:16:42,810 And each element needs to be unique. 347 00:16:42,810 --> 00:16:46,070 So if you have a collection, say, of 1, 348 00:16:46,070 --> 00:16:48,030 1, 2, 2, that's not a set. 349 00:16:48,030 --> 00:16:51,170 It has to reduce to 1 and 2. 350 00:16:54,320 --> 00:16:55,680 There's different kinds of sets. 351 00:16:55,680 --> 00:16:59,540 You can have your empty set, which is represented 352 00:16:59,540 --> 00:17:02,580 by the 0, the cross. 353 00:17:02,580 --> 00:17:06,960 There is a set with an infinite number of elements. 354 00:17:06,960 --> 00:17:09,170 An example of this is a set of integers. 355 00:17:09,170 --> 00:17:14,280 It can go on negative 1, 0, 1, 2, et cetera, et cetera. 356 00:17:14,280 --> 00:17:17,104 So even though it's not a finite number of objects, 357 00:17:17,104 --> 00:17:18,270 it's still considered a set. 358 00:17:21,510 --> 00:17:22,560 You can have subsets. 359 00:17:22,560 --> 00:17:30,630 So if you have a set H, then H is a subset of G 360 00:17:30,630 --> 00:17:36,520 if every element in H is in G. So if H was a set of 1 and 2, 361 00:17:36,520 --> 00:17:40,200 then that's a subset of G as well. 362 00:17:40,200 --> 00:17:43,710 And if every element in G is a subset of H, 363 00:17:43,710 --> 00:17:46,370 then that means they're equal. 364 00:17:46,370 --> 00:17:48,960 And then you have your universal set, 365 00:17:48,960 --> 00:17:54,030 which is symbolized by the omega there. 366 00:17:54,030 --> 00:17:56,370 And that means it contains all the elements 367 00:17:56,370 --> 00:18:01,630 possible in your problem context. 368 00:18:01,630 --> 00:18:06,900 So this is a more graphical look at it. 369 00:18:09,450 --> 00:18:13,080 So assuming that your universal set for this context 370 00:18:13,080 --> 00:18:19,170 is all numbers, then you have 1,053.6-- 371 00:18:19,170 --> 00:18:22,080 or any number-- and then your set G 372 00:18:22,080 --> 00:18:24,270 would be all the integers. 373 00:18:24,270 --> 00:18:28,470 And then H, which has 1 and 2, would be your subset of G. 374 00:18:28,470 --> 00:18:33,980 So G encompasses H. And does that make sense to everyone? 375 00:18:37,980 --> 00:18:43,010 There are set operations you can perform. 376 00:18:43,010 --> 00:18:45,950 First one is complement of S, which, oh, 377 00:18:45,950 --> 00:18:51,050 S is just a random set called S. So complement of S 378 00:18:51,050 --> 00:18:53,960 means all the elements that are not in S. 379 00:18:53,960 --> 00:18:58,640 So the red here means that those are 380 00:18:58,640 --> 00:19:03,590 the shaded areas that are not in S but are in the universal set. 381 00:19:03,590 --> 00:19:05,290 Is that clear to everyone? 382 00:19:05,290 --> 00:19:06,230 OK. 383 00:19:06,230 --> 00:19:09,260 And then the second one is union of sets, which means 384 00:19:09,260 --> 00:19:13,080 all elements in S or T or both. 385 00:19:13,080 --> 00:19:16,260 And that's symbolized by that U right there. 386 00:19:16,260 --> 00:19:23,750 So if you had a set that had 1 and 2, and then T had 2 and 3, 387 00:19:23,750 --> 00:19:26,870 then your union of sets is 1, 2, and 3. 388 00:19:26,870 --> 00:19:30,020 So you don't count 2 twice, because elements of the set 389 00:19:30,020 --> 00:19:30,920 have to be unique. 390 00:19:30,920 --> 00:19:31,650 Right? 391 00:19:31,650 --> 00:19:34,040 OK. 392 00:19:34,040 --> 00:19:35,960 And then your intersection of sets 393 00:19:35,960 --> 00:19:40,340 means all the elements of both S and T. So given that example 394 00:19:40,340 --> 00:19:45,840 I had before, then your intersection would only be 2. 395 00:19:45,840 --> 00:19:48,490 So does that makes sense, everyone? 396 00:19:48,490 --> 00:19:50,530 OK. 397 00:19:50,530 --> 00:19:53,740 So I just want to make sure you guys get it. 398 00:19:56,320 --> 00:19:58,579 Can anyone tell me what the first one is? 399 00:20:05,454 --> 00:20:07,120 AUDIENCE: The system is giving me shade. 400 00:20:07,120 --> 00:20:08,108 Do you want the shade? 401 00:20:08,108 --> 00:20:08,858 VINA NGUYEN: Yeah. 402 00:20:08,858 --> 00:20:10,737 AUDIENCE: OK, so complement of S. 403 00:20:10,737 --> 00:20:11,570 VINA NGUYEN: Mm-hmm. 404 00:20:11,570 --> 00:20:12,420 And the second one? 405 00:20:15,217 --> 00:20:15,717 Yeah? 406 00:20:15,717 --> 00:20:18,550 AUDIENCE: Complement of T? 407 00:20:18,550 --> 00:20:19,961 VINA NGUYEN: You sure? 408 00:20:19,961 --> 00:20:20,460 Oh, sorry. 409 00:20:20,460 --> 00:20:22,625 The second one is this one, right? 410 00:20:22,625 --> 00:20:23,125 Yeah. 411 00:20:23,125 --> 00:20:23,666 AUDIENCE: OK. 412 00:20:26,850 --> 00:20:30,000 VINA NGUYEN: So complement of T would mean 413 00:20:30,000 --> 00:20:32,710 this area and that area, right? 414 00:20:32,710 --> 00:20:36,130 But because T is shaded, it can't mean 415 00:20:36,130 --> 00:20:42,910 not T. Can anyone help her? 416 00:20:46,670 --> 00:20:53,840 AUDIENCE: Is it complement of S plus union of S and T? 417 00:20:53,840 --> 00:20:54,890 VINA NGUYEN: Yep. 418 00:20:54,890 --> 00:20:56,890 Can anyone see that? 419 00:20:56,890 --> 00:20:58,930 I'll just write the answers. 420 00:21:03,480 --> 00:21:03,980 OK. 421 00:21:03,980 --> 00:21:07,040 So your first one was SC. 422 00:21:07,040 --> 00:21:09,530 Can everyone see this? 423 00:21:09,530 --> 00:21:10,830 Can everyone see this? 424 00:21:10,830 --> 00:21:12,670 OK. 425 00:21:12,670 --> 00:21:18,170 So you said, complement of S, union T, right? 426 00:21:18,170 --> 00:21:20,950 Does everyone see why that's right? 427 00:21:20,950 --> 00:21:22,754 Your complement of S would be, like, 428 00:21:22,754 --> 00:21:24,170 AUDIENCE: Kind of an intersection. 429 00:21:24,170 --> 00:21:24,836 VINA NGUYEN: Hm? 430 00:21:24,836 --> 00:21:28,090 AUDIENCE: Yeah, it's kind of an intersection. 431 00:21:28,090 --> 00:21:29,460 VINA NGUYEN: Oh, OK. 432 00:21:29,460 --> 00:21:30,848 Well, it's actually a union. 433 00:21:30,848 --> 00:21:33,190 Sorry. 434 00:21:33,190 --> 00:21:34,442 Wait. 435 00:21:34,442 --> 00:21:35,855 AUDIENCE: Intersection of-- 436 00:21:39,623 --> 00:21:41,879 VINA NGUYEN: Complement S, union T. Yeah, it's-- 437 00:21:41,879 --> 00:21:44,420 AUDIENCE: It's an intersection, which is what I meant to say. 438 00:21:44,420 --> 00:21:45,128 But I said union. 439 00:21:45,128 --> 00:21:46,580 VINA NGUYEN: Wait, sorry? 440 00:21:46,580 --> 00:21:49,156 AUDIENCE: It's intersection, but I said union by accident. 441 00:21:49,156 --> 00:21:50,711 So I think it was union. 442 00:21:50,711 --> 00:21:51,710 VINA NGUYEN: It's union. 443 00:21:51,710 --> 00:21:52,335 AUDIENCE: Yeah. 444 00:21:52,335 --> 00:21:53,370 VINA NGUYEN: Yes. 445 00:21:53,370 --> 00:21:57,400 Because if you said union and T, then none of this could count. 446 00:21:57,400 --> 00:21:58,027 Right? 447 00:21:58,027 --> 00:21:58,941 AUDIENCE: Oh. 448 00:21:58,941 --> 00:21:59,855 VINA NGUYEN: Yeah. 449 00:21:59,855 --> 00:22:00,894 AUDIENCE: Oh. 450 00:22:00,894 --> 00:22:02,560 VINA NGUYEN: Is that clear for everyone? 451 00:22:02,560 --> 00:22:04,494 AUDIENCE: No. 452 00:22:04,494 --> 00:22:05,160 VINA NGUYEN: OK. 453 00:22:05,160 --> 00:22:11,140 So you have your SC, right? 454 00:22:13,920 --> 00:22:18,950 Plus T. It can't-- 455 00:22:18,950 --> 00:22:19,450 OK. 456 00:22:19,450 --> 00:22:21,790 Does that make sense? 457 00:22:21,790 --> 00:22:23,550 Actually, S was this part too. 458 00:22:23,550 --> 00:22:25,810 Sorry. 459 00:22:25,810 --> 00:22:26,740 OK. 460 00:22:26,740 --> 00:22:28,780 So the third one? 461 00:22:31,750 --> 00:22:34,225 AUDIENCE: Intersection of ST-- 462 00:22:38,680 --> 00:22:39,670 VINA NGUYEN: Comp-- 463 00:22:39,670 --> 00:22:40,660 AUDIENCE: Comp-- wait. 464 00:22:46,799 --> 00:22:47,590 VINA NGUYEN: Comp-- 465 00:22:53,560 --> 00:22:54,640 Complement. 466 00:22:54,640 --> 00:22:55,769 Right? 467 00:22:55,769 --> 00:22:56,310 AUDIENCE: OK. 468 00:22:56,310 --> 00:22:56,976 VINA NGUYEN: OK. 469 00:22:56,976 --> 00:22:58,990 Did everyone hear that? 470 00:22:58,990 --> 00:23:03,020 He said it was intersection of S and T complement, 471 00:23:03,020 --> 00:23:07,246 so complement of the intersection of S and T. 472 00:23:07,246 --> 00:23:08,290 I'll do that again. 473 00:23:08,290 --> 00:23:16,892 So S union T complement. 474 00:23:16,892 --> 00:23:18,980 Does that make sense to everyone? 475 00:23:18,980 --> 00:23:20,300 OK. 476 00:23:20,300 --> 00:23:27,380 And another way you can write that is complement of S 477 00:23:27,380 --> 00:23:33,053 and complement of T. Does everyone see that? 478 00:23:33,053 --> 00:23:35,020 Yeah? 479 00:23:35,020 --> 00:23:36,180 OK. 480 00:23:36,180 --> 00:23:40,210 So 4? 481 00:23:40,210 --> 00:23:40,712 AUDIENCE: T? 482 00:23:40,712 --> 00:23:41,420 VINA NGUYEN: Yes. 483 00:23:44,660 --> 00:23:45,840 And 5? 484 00:23:54,624 --> 00:23:56,088 AUDIENCE: Union, wait. 485 00:23:56,088 --> 00:24:02,280 Union set of T, complement of T? 486 00:24:02,280 --> 00:24:05,216 VINA NGUYEN: Complement of T-- 487 00:24:05,216 --> 00:24:10,530 AUDIENCE: With the union set of S and T? 488 00:24:10,530 --> 00:24:12,646 VINA NGUYEN: Close. 489 00:24:12,646 --> 00:24:20,980 AUDIENCE: Complement of T intersection of S? 490 00:24:20,980 --> 00:24:22,020 VINA NGUYEN: Yes. 491 00:24:22,020 --> 00:24:22,520 Yeah. 492 00:24:26,304 --> 00:24:26,804 Wait. 493 00:24:29,511 --> 00:24:30,010 Yeah. 494 00:24:30,010 --> 00:24:30,870 OK. 495 00:24:30,870 --> 00:24:32,970 So that would be-- 496 00:24:32,970 --> 00:24:34,390 right? 497 00:24:34,390 --> 00:24:35,230 OK. 498 00:24:35,230 --> 00:24:37,230 Does everyone see that? 499 00:24:37,230 --> 00:24:38,410 OK. 500 00:24:38,410 --> 00:24:39,728 And the sixth one? 501 00:24:43,214 --> 00:24:45,369 AUDIENCE: Complement of the union of S and T? 502 00:24:45,369 --> 00:24:46,202 VINA NGUYEN: Mm-hmm. 503 00:24:50,190 --> 00:24:54,610 And given this example, can anyone tell me a different way 504 00:24:54,610 --> 00:24:56,150 to write the sixth one? 505 00:24:59,498 --> 00:24:59,998 Oh. 506 00:24:59,998 --> 00:25:04,810 AUDIENCE: Complement of S and the union as a complement of T? 507 00:25:04,810 --> 00:25:05,822 VINA NGUYEN: This one? 508 00:25:05,822 --> 00:25:06,220 AUDIENCE: Intersect. 509 00:25:06,220 --> 00:25:06,906 VINA NGUYEN: Intersect. 510 00:25:06,906 --> 00:25:07,620 AUDIENCE: And the intersection. 511 00:25:07,620 --> 00:25:08,370 VINA NGUYEN: Yeah. 512 00:25:10,730 --> 00:25:11,230 OK. 513 00:25:11,230 --> 00:25:12,530 Does everyone see that? 514 00:25:12,530 --> 00:25:14,150 OK. 515 00:25:14,150 --> 00:25:17,590 So that is a very abstract thing, 516 00:25:17,590 --> 00:25:21,790 but it's very fundamental or everything else 517 00:25:21,790 --> 00:25:24,161 doesn't make sense. 518 00:25:24,161 --> 00:25:24,660 OK. 519 00:25:24,660 --> 00:25:30,300 So probability models, your sample space is like a set, 520 00:25:30,300 --> 00:25:31,290 right? 521 00:25:31,290 --> 00:25:34,530 You need to know what are all the possible outcomes. 522 00:25:34,530 --> 00:25:37,585 So that would be your universal set. 523 00:25:37,585 --> 00:25:39,630 It has to be exhaustive. 524 00:25:39,630 --> 00:25:42,120 You can't leave out any events or your probabilities 525 00:25:42,120 --> 00:25:43,870 will not be correct. 526 00:25:43,870 --> 00:25:45,765 And none of the events can overlap. 527 00:25:48,820 --> 00:25:51,880 So every result that can happen has 528 00:25:51,880 --> 00:25:54,790 to be uniquely defined within your context. 529 00:25:58,000 --> 00:26:00,550 And then the events are a subset of your sample space. 530 00:26:00,550 --> 00:26:03,270 They don't necessarily have to be like probability 531 00:26:03,270 --> 00:26:04,630 of die being 1. 532 00:26:04,630 --> 00:26:08,954 They could be probability of your result being even. 533 00:26:08,954 --> 00:26:10,870 So it doesn't necessarily have to be just one. 534 00:26:10,870 --> 00:26:14,090 It can be a couple of events that can happen. 535 00:26:14,090 --> 00:26:16,330 And you also need probabilities. 536 00:26:16,330 --> 00:26:18,685 So that's your quantitative measure of the problem. 537 00:26:21,320 --> 00:26:25,120 So if you were to model rolling just one die, 538 00:26:25,120 --> 00:26:27,160 what would your sample space be? 539 00:26:30,548 --> 00:26:32,968 Anyone? 540 00:26:32,968 --> 00:26:35,388 AUDIENCE: It would be numbers 1 through 6. 541 00:26:35,388 --> 00:26:36,370 VINA NGUYEN: Yup. 542 00:26:36,370 --> 00:26:39,070 And what kind of events would you have? 543 00:26:43,250 --> 00:26:47,370 Like, event that you roll a 1? 544 00:26:47,370 --> 00:26:50,342 Is there any other kind of event? 545 00:26:50,342 --> 00:26:53,180 AUDIENCE: In general you can conclude-- 546 00:26:53,180 --> 00:26:54,130 VINA NGUYEN: Yup. 547 00:26:54,130 --> 00:26:57,340 Or it could be, like, an event that you roll greater than 4, 548 00:26:57,340 --> 00:26:59,392 or something like that. 549 00:26:59,392 --> 00:27:01,100 And then you need probabilities for that. 550 00:27:01,100 --> 00:27:03,280 So even number would be like one half. 551 00:27:03,280 --> 00:27:05,450 Greater than 4 would be like one third. 552 00:27:05,450 --> 00:27:08,770 Or probably of 1 would be one sixth. 553 00:27:08,770 --> 00:27:11,950 So what if you needed to do two die? 554 00:27:11,950 --> 00:27:16,670 Then how would you represent what that problem space is? 555 00:27:21,966 --> 00:27:22,466 Anyone? 556 00:27:25,847 --> 00:27:27,697 AUDIENCE: Doesn't it depend on what event 557 00:27:27,697 --> 00:27:29,230 you're talking about? 558 00:27:29,230 --> 00:27:32,084 If you wanted to do sum, then it'd be 2, 12. 559 00:27:32,084 --> 00:27:37,740 But if you wanted to do pairs, then it'd be one-- 560 00:27:37,740 --> 00:27:40,260 VINA NGUYEN: So that would be events. 561 00:27:40,260 --> 00:27:42,100 But in terms of sample space, you only 562 00:27:42,100 --> 00:27:44,100 can have certain results that come out 563 00:27:44,100 --> 00:27:47,000 from your die, which would be the combination of numbers. 564 00:27:47,000 --> 00:27:47,500 Right? 565 00:27:47,500 --> 00:27:49,970 AUDIENCE: Oh, so we're talking about confirmation as-- 566 00:27:49,970 --> 00:27:51,946 because couldn't you also base it off, like, 567 00:27:51,946 --> 00:27:54,859 what's the chance that the numbers are the same? 568 00:27:54,859 --> 00:27:55,650 VINA NGUYEN: Right. 569 00:27:55,650 --> 00:27:59,160 So that would be an event, but not part of your sample space. 570 00:27:59,160 --> 00:28:03,120 Because your sample space is the actual, physical results 571 00:28:03,120 --> 00:28:06,930 that could happen, like a 1 and a 1, a 1 and a 3. 572 00:28:06,930 --> 00:28:09,740 And then how you interpret that is an event. 573 00:28:09,740 --> 00:28:11,640 AUDIENCE: OK. 574 00:28:11,640 --> 00:28:16,530 VINA NGUYEN: So I guess I'd kind of given it, but-- 575 00:28:21,799 --> 00:28:23,694 Where's my chalk? 576 00:28:23,694 --> 00:28:24,194 Hm? 577 00:28:24,194 --> 00:28:25,735 AUDIENCE: It would both be the same-- 578 00:28:25,735 --> 00:28:27,220 AUDIENCE: Wouldn't it be the same? 579 00:28:27,220 --> 00:28:29,428 VINA NGUYEN: It would not be the same, because you're 580 00:28:29,428 --> 00:28:30,310 rolling two, right? 581 00:28:30,310 --> 00:28:32,302 AUDIENCE: The solution-- 582 00:28:32,302 --> 00:28:34,792 VINA NGUYEN: Yeah. 583 00:28:34,792 --> 00:28:35,940 AUDIENCE: So the expert's-- 584 00:28:35,940 --> 00:28:36,690 VINA NGUYEN: Yeah. 585 00:28:36,690 --> 00:28:38,119 AUDIENCE: It's gonna be one-- 586 00:28:38,119 --> 00:28:38,910 VINA NGUYEN: Right. 587 00:28:38,910 --> 00:28:40,450 So I'll get to that later. 588 00:28:40,450 --> 00:28:43,840 But the more basic thing-- 589 00:28:43,840 --> 00:28:44,790 can you guys see this? 590 00:28:44,790 --> 00:28:45,443 I don't-- 591 00:28:45,443 --> 00:28:46,270 AUDIENCE: Kind of. 592 00:28:46,270 --> 00:28:47,144 VINA NGUYEN: Kind of. 593 00:28:47,144 --> 00:28:56,560 I'll just-- so you were right about representing it. 594 00:28:56,560 --> 00:28:58,780 But for what it actually is, your sample space 595 00:28:58,780 --> 00:29:02,810 would be like 1, 1. 596 00:29:02,810 --> 00:29:03,520 Right? 597 00:29:03,520 --> 00:29:05,890 That would be the roll of your first die, 598 00:29:05,890 --> 00:29:07,472 the role is your second die. 599 00:29:07,472 --> 00:29:08,890 AUDIENCE: Oh, so you'll-- 600 00:29:08,890 --> 00:29:10,650 VINA NGUYEN: Yeah, just really basic. 601 00:29:10,650 --> 00:29:11,950 Yeah. 602 00:29:11,950 --> 00:29:13,220 Like that. 603 00:29:13,220 --> 00:29:14,815 So that's your sample space. 604 00:29:14,815 --> 00:29:15,480 AUDIENCE: Oh. 605 00:29:15,480 --> 00:29:16,230 VINA NGUYEN: Yeah. 606 00:29:16,230 --> 00:29:17,511 AUDIENCE: Do you write it on-- 607 00:29:17,511 --> 00:29:18,760 VINA NGUYEN: I'm not going to. 608 00:29:18,760 --> 00:29:22,500 I can assume that you guys can figure that out. 609 00:29:22,500 --> 00:29:26,330 But is that clear how that's separate from an actual event? 610 00:29:26,330 --> 00:29:27,351 Yeah? 611 00:29:27,351 --> 00:29:27,850 OK. 612 00:29:27,850 --> 00:29:30,250 Right So that would be your sample space. 613 00:29:30,250 --> 00:29:34,635 But like what you mentioned, what's your name? 614 00:29:34,635 --> 00:29:35,260 AUDIENCE: Mine? 615 00:29:35,260 --> 00:29:35,795 VINA NGUYEN: Yeah. 616 00:29:35,795 --> 00:29:36,130 AUDIENCE: [INAUDIBLE] 617 00:29:36,130 --> 00:29:36,400 VINA NGUYEN: OK. 618 00:29:36,400 --> 00:29:38,560 What [INAUDIBLE] mentioned is that the events-- 619 00:29:42,310 --> 00:29:48,880 the probability that your sum is 12, that's an event. 620 00:29:48,880 --> 00:29:51,550 But that's not part of your sample space. 621 00:29:51,550 --> 00:29:54,450 Is that clear how that's different? 622 00:29:54,450 --> 00:29:56,895 Or the probability that you get doubles-- 623 00:30:06,150 --> 00:30:08,670 so do you guys understand difference 624 00:30:08,670 --> 00:30:11,460 between your physical sample space 625 00:30:11,460 --> 00:30:13,670 and the different kind of events you can get from it? 626 00:30:13,670 --> 00:30:16,890 AUDIENCE: Is the sample space include exact values 627 00:30:16,890 --> 00:30:19,440 that you actually can get it? 628 00:30:19,440 --> 00:30:20,820 VINA NGUYEN: Your exact outcome. 629 00:30:20,820 --> 00:30:22,835 The bare bone. 630 00:30:22,835 --> 00:30:24,960 And then your events would be how you interpret it. 631 00:30:28,446 --> 00:30:30,440 Is that good? 632 00:30:30,440 --> 00:30:32,080 OK. 633 00:30:32,080 --> 00:30:34,386 And the probability is just like what's 634 00:30:34,386 --> 00:30:35,760 the probability this will happen? 635 00:30:35,760 --> 00:30:37,426 What's the probability that will happen? 636 00:30:37,426 --> 00:30:38,810 I know this is one sixth. 637 00:30:38,810 --> 00:30:40,980 I will figure that out later. 638 00:30:40,980 --> 00:30:42,120 OK. 639 00:30:42,120 --> 00:30:48,360 So going back to what you said, how you represent this 640 00:30:48,360 --> 00:30:52,470 is pretty much up to you. 641 00:30:52,470 --> 00:30:56,124 The standard way is what you mentioned. 642 00:30:56,124 --> 00:30:57,290 What were you saying, again? 643 00:30:57,290 --> 00:31:01,772 AUDIENCE: The table where that has one that sits on top. 644 00:31:01,772 --> 00:31:03,219 And this-- 645 00:31:03,219 --> 00:31:04,010 VINA NGUYEN: Right. 646 00:31:04,010 --> 00:31:06,030 So you're talking about this. 647 00:31:06,030 --> 00:31:06,530 Right? 648 00:31:08,595 --> 00:31:09,470 Is that what you're-- 649 00:31:09,470 --> 00:31:10,000 AUDIENCE: Yeah. 650 00:31:10,000 --> 00:31:10,210 VINA NGUYEN: Yeah. 651 00:31:10,210 --> 00:31:10,709 OK. 652 00:31:13,780 --> 00:31:15,772 So this would be your first die. 653 00:31:15,772 --> 00:31:17,160 AUDIENCE: OK. 654 00:31:17,160 --> 00:31:20,660 VINA NGUYEN: And this would be your second. 655 00:31:20,660 --> 00:31:33,620 One, two-- OK. 656 00:31:33,620 --> 00:31:37,010 So that's one way to represent your outcomes, right? 657 00:31:37,010 --> 00:31:42,875 So the probability of doubles would be these diagonals. 658 00:31:42,875 --> 00:31:44,360 Does everyone see that? 659 00:31:44,360 --> 00:31:45,250 OK. 660 00:31:45,250 --> 00:31:48,070 And then 12-- oh, there's just one. 661 00:31:48,070 --> 00:31:49,425 OK. 662 00:31:49,425 --> 00:31:52,090 So that's easy. 663 00:31:52,090 --> 00:31:55,010 Is there another way to represent sample space? 664 00:31:58,380 --> 00:32:01,940 I just left that there so you guys can draw. 665 00:32:01,940 --> 00:32:05,540 Is there another way to represent how 666 00:32:05,540 --> 00:32:08,690 your experiment will progress? 667 00:32:08,690 --> 00:32:10,389 AUDIENCE: Graph? 668 00:32:10,389 --> 00:32:11,180 VINA NGUYEN: Graph? 669 00:32:11,180 --> 00:32:12,138 How would you graph it? 670 00:32:12,138 --> 00:32:19,250 AUDIENCE: Like 1 through 6 on the x-axis, and-- 671 00:32:19,250 --> 00:32:21,310 VINA NGUYEN: So it's kind of like this, 672 00:32:21,310 --> 00:32:24,010 except it's like a grid. 673 00:32:24,010 --> 00:32:25,610 You would just put it here. 674 00:32:25,610 --> 00:32:26,550 Right? 675 00:32:26,550 --> 00:32:28,200 So, yes, you're right. 676 00:32:28,200 --> 00:32:30,900 But it's like this already. 677 00:32:30,900 --> 00:32:31,810 Is there another way? 678 00:32:38,796 --> 00:32:39,877 How much time we have? 679 00:32:43,290 --> 00:32:47,820 Well, what if you did a tree? 680 00:32:47,820 --> 00:32:49,740 So you roll it once. 681 00:32:49,740 --> 00:32:51,460 You get a 1. 682 00:32:51,460 --> 00:32:53,400 You get a 2. 683 00:32:53,400 --> 00:33:01,670 You get a 3, 4, 5, 6. 684 00:33:01,670 --> 00:33:04,430 And then you would just expand this-- 685 00:33:04,430 --> 00:33:05,200 1, 2. 686 00:33:10,020 --> 00:33:11,000 Right? 687 00:33:11,000 --> 00:33:14,250 So that's just another way to keep in mind. 688 00:33:14,250 --> 00:33:17,160 For this example, it grows exponentially. 689 00:33:17,160 --> 00:33:18,830 So it's not the best way. 690 00:33:18,830 --> 00:33:22,130 But it is a good way for certain contexts. 691 00:33:22,130 --> 00:33:25,070 So does everyone see how that works? 692 00:33:25,070 --> 00:33:25,570 OK. 693 00:33:32,570 --> 00:33:35,810 And we ended kind of short, because I wasn't sure 694 00:33:35,810 --> 00:33:37,790 how long this would take. 695 00:33:37,790 --> 00:33:41,270 So I want to make sure you guys know why we study probability. 696 00:33:41,270 --> 00:33:43,400 There's lots of reasons out there. 697 00:33:43,400 --> 00:33:45,450 There's two different definitions. 698 00:33:45,450 --> 00:33:47,990 I know that's not entirely intuitive. 699 00:33:47,990 --> 00:33:50,060 So it's either how often something 700 00:33:50,060 --> 00:33:54,170 happens given a number of repeatable experiments, 701 00:33:54,170 --> 00:33:58,520 or the second definition, how much you believe that something 702 00:33:58,520 --> 00:34:01,850 will happen given the evidence. 703 00:34:01,850 --> 00:34:03,440 And then basic set theory, you guys 704 00:34:03,440 --> 00:34:05,250 seem to pretty much know that. 705 00:34:05,250 --> 00:34:07,896 I wasn't sure how much knowledge you guys had. 706 00:34:07,896 --> 00:34:09,270 But if you do have any questions, 707 00:34:09,270 --> 00:34:10,949 don't hesitate to email me. 708 00:34:10,949 --> 00:34:14,850 I can go over that with you. 709 00:34:14,850 --> 00:34:17,659 And probability models are important. 710 00:34:17,659 --> 00:34:24,290 So you can take a certain puzzle or problem context in your mind 711 00:34:24,290 --> 00:34:26,510 and graph it out in something that you can actually 712 00:34:26,510 --> 00:34:27,110 work with. 713 00:34:29,940 --> 00:34:34,820 So does anyone have questions or anything 714 00:34:34,820 --> 00:34:37,810 about the class, probability, HSSB? 715 00:34:43,320 --> 00:34:46,055 Was this too fast or too slow? 716 00:34:46,055 --> 00:34:48,650 I'm not really sure the knowledge you 717 00:34:48,650 --> 00:34:52,058 guys have beforehand. 718 00:34:52,058 --> 00:34:53,042 No? 719 00:34:53,042 --> 00:34:54,520 AUDIENCE: I think it's a good pace. 720 00:34:54,520 --> 00:34:55,478 VINA NGUYEN: Good pace? 721 00:34:55,478 --> 00:34:56,150 OK. 722 00:34:56,150 --> 00:34:57,830 Next time I'll fill up the time. 723 00:34:57,830 --> 00:34:58,330 Sorry. 724 00:34:58,330 --> 00:35:02,270 I wasn't sure how long registration was going to take. 725 00:35:02,270 --> 00:35:04,270 AUDIENCE: Could we go over set operations again? 726 00:35:04,270 --> 00:35:04,978 VINA NGUYEN: Yup. 727 00:35:12,026 --> 00:35:12,530 OK. 728 00:35:12,530 --> 00:35:14,850 So do you have a certain question 729 00:35:14,850 --> 00:35:16,019 or just want to go over it? 730 00:35:16,019 --> 00:35:16,560 AUDIENCE: No. 731 00:35:16,560 --> 00:35:17,227 Just in general. 732 00:35:17,227 --> 00:35:18,434 VINA NGUYEN: Just in general? 733 00:35:18,434 --> 00:35:19,130 OK. 734 00:35:19,130 --> 00:35:23,910 So do you know what a universal set is? 735 00:35:27,060 --> 00:35:30,300 All the possible things that can happen is a universal set. 736 00:35:30,300 --> 00:35:32,250 And if you have a set-- 737 00:35:37,870 --> 00:35:44,190 so say your set is all the combinations that are doubles. 738 00:35:44,190 --> 00:35:55,662 So S would be like 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6. 739 00:35:55,662 --> 00:36:01,730 So this would be set S. And then complement of S 740 00:36:01,730 --> 00:36:05,210 is anything that's not an S. So that would mean anything here 741 00:36:05,210 --> 00:36:07,830 that's not a double. 742 00:36:07,830 --> 00:36:09,420 Does that make sense? 743 00:36:09,420 --> 00:36:11,340 So a complement of S is anything that's 744 00:36:11,340 --> 00:36:15,140 not in S but within your universal problem context. 745 00:36:18,440 --> 00:36:19,030 Good? 746 00:36:19,030 --> 00:36:19,870 OK. 747 00:36:19,870 --> 00:36:21,730 So union of sets means that if you 748 00:36:21,730 --> 00:36:24,010 have two different kinds of sets, 749 00:36:24,010 --> 00:36:38,092 it's everything in S and T. So T could be that you rolled a 6 750 00:36:38,092 --> 00:36:39,050 in either one of these. 751 00:36:39,050 --> 00:36:47,560 So this would be T. And this would be T. Can you see that? 752 00:36:47,560 --> 00:36:49,900 I'm sorry it's a little messy. 753 00:36:49,900 --> 00:36:54,820 So your union would be this block, this block, this block, 754 00:36:54,820 --> 00:36:59,070 this block, this block, this block, everything here, 755 00:36:59,070 --> 00:37:00,640 and everything here. 756 00:37:00,640 --> 00:37:04,360 So that would be your union. 757 00:37:04,360 --> 00:37:06,160 And like I said before, even though you 758 00:37:06,160 --> 00:37:08,320 might have an element in both sets, 759 00:37:08,320 --> 00:37:10,540 when you do write out your set, you only 760 00:37:10,540 --> 00:37:15,160 count it once, because every element has to be unique. 761 00:37:15,160 --> 00:37:17,650 OK? 762 00:37:17,650 --> 00:37:19,720 AUDIENCE: Does T stand for something or just 763 00:37:19,720 --> 00:37:20,550 like a random name? 764 00:37:20,550 --> 00:37:22,091 VINA NGUYEN: T is just a random name. 765 00:37:22,091 --> 00:37:27,020 You can be like, set A, set B, set XYZ. 766 00:37:27,020 --> 00:37:28,940 I just did it because it's the next letter 767 00:37:28,940 --> 00:37:33,880 after S. Is that good? 768 00:37:33,880 --> 00:37:34,580 OK. 769 00:37:34,580 --> 00:37:39,980 So your intersection of sets is anything that is in both. 770 00:37:39,980 --> 00:37:42,350 And given this example, the only thing that's in both 771 00:37:42,350 --> 00:37:44,360 would be 6, 6. 772 00:37:44,360 --> 00:37:45,140 Right? 773 00:37:45,140 --> 00:37:48,700 So your intersection would be just 6, 774 00:37:48,700 --> 00:37:58,790 6 equals S intersect with T. OK? 775 00:37:58,790 --> 00:38:01,170 Is that clear? 776 00:38:01,170 --> 00:38:04,500 Did you guys have any other questions about these things? 777 00:38:04,500 --> 00:38:06,000 AUDIENCE: I want to know about that. 778 00:38:06,000 --> 00:38:06,210 VINA NGUYEN: OK. 779 00:38:06,210 --> 00:38:06,706 Go ahead. 780 00:38:06,706 --> 00:38:07,706 AUDIENCE: Does it mean-- 781 00:38:07,706 --> 00:38:12,162 could you give us an example for it using probability 782 00:38:12,162 --> 00:38:14,150 in a situation? 783 00:38:14,150 --> 00:38:15,490 VINA NGUYEN: OK. 784 00:38:15,490 --> 00:38:21,170 So there was a pretty simple example 785 00:38:21,170 --> 00:38:24,200 I gave you about how confident am I 786 00:38:24,200 --> 00:38:26,660 that I'm going to get an A or something, right? 787 00:38:26,660 --> 00:38:33,640 But another basic example is like say 788 00:38:33,640 --> 00:38:37,610 you notice that your neighbor's grass was wet 789 00:38:37,610 --> 00:38:39,220 when you came home. 790 00:38:39,220 --> 00:38:42,820 And that's an event, but you're not sure whether it was 791 00:38:42,820 --> 00:38:46,000 because of their sprinkler, or because it was thunder-storming 792 00:38:46,000 --> 00:38:49,690 this morning, or because-- 793 00:38:49,690 --> 00:38:51,790 I don't know-- there was a flood. 794 00:38:51,790 --> 00:38:53,710 So you have to take the probability of each 795 00:38:53,710 --> 00:38:57,569 of those previous events, like, what's the probability that he 796 00:38:57,569 --> 00:38:58,235 has a sprinkler? 797 00:38:58,235 --> 00:39:02,680 If it's 0, then you can say that's less likely unless he 798 00:39:02,680 --> 00:39:05,200 got one today or something. 799 00:39:05,200 --> 00:39:07,990 Or if you live in California, the probability 800 00:39:07,990 --> 00:39:09,700 of a thunderstorm is lower, so you also 801 00:39:09,700 --> 00:39:14,626 can get a sense for how likely it was a thunderstorm or not. 802 00:39:14,626 --> 00:39:15,125 Right? 803 00:39:17,612 --> 00:39:19,070 I don't about floods in California, 804 00:39:19,070 --> 00:39:20,410 but it's kind of like that. 805 00:39:20,410 --> 00:39:22,450 You have previous probabilities that you 806 00:39:22,450 --> 00:39:26,440 know about that are related to your current problem, 807 00:39:26,440 --> 00:39:29,410 but you can't exactly know. 808 00:39:29,410 --> 00:39:35,080 But you can quantify it given the previous evidence. 809 00:39:35,080 --> 00:39:35,980 Does that make sense? 810 00:39:35,980 --> 00:39:36,563 AUDIENCE: Yes. 811 00:39:36,563 --> 00:39:38,430 VINA NGUYEN: OK. 812 00:39:38,430 --> 00:39:39,410 Anybody else? 813 00:39:45,780 --> 00:39:49,690 Or any other non set questions or set questions? 814 00:39:55,570 --> 00:39:56,070 No? 815 00:39:56,070 --> 00:39:56,770 OK. 816 00:39:56,770 --> 00:39:59,710 Well, I guess you guys can just finish off the cookies. 817 00:39:59,710 --> 00:40:02,340 And if you do have questions, then 818 00:40:02,340 --> 00:40:04,410 you can come to me right now after class, 819 00:40:04,410 --> 00:40:06,960 or you can email me. 820 00:40:06,960 --> 00:40:08,930 My name is Vina, again. 821 00:40:08,930 --> 00:40:12,820 And I hope you guys have a good rest of the day. 822 00:40:12,820 --> 00:40:13,320 Oh, yeah. 823 00:40:13,320 --> 00:40:15,050 You guys should go back to Lobby 13 824 00:40:15,050 --> 00:40:17,420 at 3:00 so you can choose your labs class. 825 00:40:17,420 --> 00:40:20,120 OK? 826 00:40:20,120 --> 00:40:21,670 Yup.