1 Teacher: okay
3 Teacher: SNAME?
5 Teacher: you what
7 Teacher: yeah are you borrowing or buying. I can sell you one for ten p.
9 Teacher: okay. listen up then guys.
11 Teacher: okay thank you today okay, tomorrow I'm not in, so we'll be, you'll be carrying on with the work that you did yesterday er as I've told you before, because you need to do that, and that's why I've set that up, so you can carry on with that tomorrow. um. today though I wanted to look a little bit at probability. okay. we've done some of this before and I wanted to push you on a little bit further with some of the probability work that we've done. so. first thing is it is my birthday today so I thought we'd play a game to start off with
13 Teacher: okay and then we'll do something else to start with.
16 Teacher: it involves cups, very observant
18 Teacher: nothing right. okay ten SNAME ten count them up good okay okay ten cups. one of them has a giant red cross on the inside, what's the probability of choosing the red cross SNAME?
20 Teacher: one in ten. SNAME choose a cup please.
22 Teacher: no go on you choose
24 Teacher: this one over here.
26 Teacher: nope no red cross so now probability what's the probability of choosing a red cup now. SNAME
28 Teacher: one in nine so has that gone up or gone down
30 Teacher: probability's gone
34 Teacher: probabilitys gone up, it's more likely now that you're going to get the red cross so SNAME choose one
36 Teacher: that one
38 Teacher: okay
40 Teacher: there is!
43 Teacher: er SNAME.
45 Teacher: one in eight. we're still going up. it's getting more likely now that we're going to get it we're going to get it right. number it one to eight that way. which one do you want
47 Teacher: so number three then
51 Teacher: yep well done right we'll play again, you have a lollipop.
53 Teacher: okay starting again the probabilities don't matter now we're going the same probabilities. guys. okay my next question would be okay is it better, is it better to go first, or is it better to hang on and wait. what's more likely. when are you going to be more likely to win if you wait if you go first? if you go last? if you go somewhere in the middle. where's the best position to actually have a guess do you think. SNAME
55 Teacher: half way through
58 Teacher: but how do you know ((inaudible)) but how do you know. half way through is five people, isn't it
60 Teacher: and SNAME was like the third person to go
62 Teacher: so you might
64 Teacher: you might lose because someone might already win. so I want you to think about what do you think the best place to actually choose is.
67 Teacher: where do you reckon
69 Teacher: go on you choose one
71 Teacher: in one of the first four. go on then you choose one.
73 Teacher: one to ten
75 Teacher: that one
78 Teacher: ah SNAME
80 Teacher: one to nine to nine
82 Teacher: the ninth one. SNAME
84 Teacher: the fifth one. I don't know which one it is, so I haven't got a clue. so we'll do that SNAME
88 Teacher: okay so. we said go in the first four. didn't you. now four people have gone.
90 Teacher: okay SNAME
92 Teacher: I've got one to six now.
94 Teacher: five left. I can shuffle them ((inaudible)) SNAME
96 Teacher: ((inaudible)) dropped it on the floor somewhere. hopefully not
98 Teacher: count them four left, one to four SNAME
100 Teacher: third
103 Teacher: how do you know which one, there's no dent in any of them
106 Teacher: they've all got, they've all got they've all got dents on the top
107 Teacher: down to three. SNAME
110 Teacher: so the middle one.
117 Teacher: so,
119 Teacher: what's the probability?
123 Teacher: fifty fifty, a half, good
125 Teacher: er if nobody wins do I get to keep the lollipop. SNAME,
128 Teacher: yeah
129 Teacher: left or right
131 Teacher: my left or your right
133 Teacher: my left
135 Teacher: this one
139 Teacher: so he had. we got down to the point where SNAME had a fifty fifty chance of winning. now. what I want to introduce you to today. well let's, let's put a question on the board. what would be? start again, what would be the probability if I had two dices of rolling two sixes let's we're talking about a total of twelve aren't we if we had two dice, what would be the probability of rolling two sixes on two dice, SNAME,
141 Teacher: one in twelve no yes
143 Teacher: nope
145 Teacher: no, what if if you rolled two sixes and you got about ten you'd get five of each. two sixes on two dice it's very unlike it's not, unlikely if you know what I mean, yep
147 Teacher: no, anybody else?
149 Teacher: good thank you SNAME. okay. what's the probability of rolling one six
153 Teacher: one in six. okay. imagine then I had two dice. I could get a one two three four five six on the first dice, a one two three four five six on the second dice okay. if I filled that in and did all the totals how many answers would I have
155 Teacher: thirty-six. good. how many would have the number twelve in?
157 Teacher: one. okay. what number would be most likely do you think. what total would be most likely
160 Teacher: what total will go
163 Teacher: what total would go diagonally across the board
166 Teacher: seven good. seven would be the most likely and there'd be six of those out of a total of thirty-six, so. how do we get one out of thirty six quickly if we know the probability of getting a six is one sixth.
168 Teacher: won't times it by six! SNAME.
170 Teacher: what do you mean put it on two sixes
172 Teacher: yeah but how do we get to this probability from this. SNAME.
174 Teacher: I do square it. okay. I am actually squaring it. but, if I said the probability of six is one sixth. that's my first dice. my second dice is one sixth. then to get the probability of getting them both. we call this the and rule. we do the probability of getting both is one sixth times one sixth. if I want the probability of both things happening. then, I want one sixth times one sixth which is one over thirty-six. we just times them together. okay?. so thinking about this as a problem. think about this when's it most likely to choose which one? okay? what's the probability of the first person winning. what's the probability of you getting it right straight away.
176 Teacher: one in ten. good. what is the probability of the second person winning. okay, think about it. what do we need the first person to do.
178 Teacher: get it wrong. so what's the probability of the first person getting it wrong.
181 Teacher: nine tenths. what's the, and, and we want the second person to win. so the probability of the second person winning is what.
186 Teacher: it doesn't matter because we're not playing at the moment, just ((inaudible))
188 Teacher: whats the probability of the second person winning?
190 Teacher: one in nine. what do I get if I multiply those together.
193 Teacher: cancel it down
196 Teacher: cancel it down again!
199 Teacher: one in ten. exactly the same probability. second person has exactly the same chance as the first person. the probability of the second person getting it is exactly the same. do it for the third, we want the first person to lose. what's the probability of the second person loosing.
202 Teacher: eight into
204 Teacher: no I've taken one away
206 Teacher: eight into nine. and then the third person winning is what
208 Teacher: one in
213 Teacher: one in eight. okay. if I cancel them down, that and that cancels. that and that cancels I'm left with a tenth. so,
215 Teacher: how do you know what this cancels down
217 Teacher: if I multiplied it out you'd see that, that I have a factor of eight on the top and a factor of eight on the bottom.
219 Teacher: and I know that because there's just an eight on the top and we're timesing them.
221 Teacher: so I can just cancel the down straight away. so, despite what you think it doesn't matter when you go. you still have the same probability if you, if you chose before now which position to go in, you would have the same probability of winning no matter where you go
223 Teacher: if I said to you line up one to ten. you could have just picked ten. if you actually were last once you got to that position ((inaudible)) opted for
226 Teacher: yes. okay. probability then, people react people think about probability too much sometimes and people don't use rational people don't necessarily use mathematics when they think about probability. before I get you to do what I want you to do today, one question. think about the national lottery. okay. a lot of people use lucky dip on the national lottery don't they.
228 Teacher: yeah? if I went to the lottery ticket and I got my lottery ticket out, my lottery machine. and I asked for a lucky dip? okay. it came out of lucky dip
230 Teacher: okay. quite a lot of people what would they say if they saw that on their lucky dip number.
233 Teacher: it's crap. no chance of winning. why?
235 Teacher: okay. right another one. which ticket would you prefer?
237 Teacher: why
242 Teacher: but which one's got a greater chance of winning.
245 Teacher: good.
248 Teacher: it goes up to forty-nine.
250 Teacher: okay. both these this is the thing about probability people don't necessarily always think mathematically they think about what they see. these have exactly the same chance of winning on the lottery
253 Teacher: exactly the same chance.
255 Teacher: what?
257 Teacher: for both of them equally
259 Teacher: it has exactly the same chance of winning
261 Teacher: okay ((inaudible)) listen again. exactly the same amount of chance of winning. okay. chance of winning with six numbers is one in thirty-six. if I pick, like we did there, if I picked out a ball at random, what's the probability of it being a three. one in forty-nine. yeah? what's the probability of it being a one.
264 Teacher: one in forty-nine. once I've picked out that number what's the probability. it will be exactly the same no matter what your numbers are.
266 Teacher: what do you mean there's less balls in the thing
268 Teacher: after you've taken out one
270 Teacher: yeah
272 Teacher: yeah but that's equally the same for both of these sets of numbers isn't it.
277 Teacher: why
284 Teacher: this are approximately
288 Teacher: no not necessarily. okay it's a one in thirteen point nine roughly million chance of both these happening. very unlikely that this is going to happen but it's also equally likely that this is going to happen. the problem is is we notice, we would notice this more wouldn't we if it came up. whereas every week we just have random numbers so you don't actually log what they are. but if you chose a set of six numbers. I don't do the lottery. if you had a set of six numbers the chance of them coming up is always exactly the same. now. today. I want you to run a little experiment for me. okay.
291 Teacher: can I just actually just ((inaudible)) sorry. no. and a probability experiment. you've done this before. it's my birthday today, and there are two other people that I actually teach. SNAME. there are two people I actually teach that also share today as their birthday
293 Teacher: yes
295 Teacher: no I just decided to make it up. okay. someone in my year ten class. someone in my tutor group both share the same birthday. does anyone share a birthday in here.
300 Teacher: yeah the twins obviously share a birthday. anybody else share a birthday
303 Teacher: SNAME?
307 Teacher: does anyone here share a birthday?
310 Teacher: okay
313 Teacher: I share a birthday with George Wellpool
317 Teacher: right, guys. okay. sh. guys listen up. okay. what I want you to do today is I'm going to get you in pairs to run an experiment for me. SNAME put that away please. okay. you're going to run an experiment to find out excuse me. I want you to run an experiment to find out how likely it is that two people in a group will share the same birthday. okay. average class size, this class, well not average class size, but this class size. normally there's about thirty people so we're going to run an experiment for about thirty people. I've got the sheets for you over here. you're going to, you gonna need a dice, which I've got for you, you're gonna need a coin,
319 Teacher: okay. so between your pair, I've got some spare coins. between your pair though, you need to find a coin
321 Teacher: you can use any coin you want,
323 Teacher: okay. sh. can I just, guys I'm going to get annoyed in a minute. okay. what you're going to do is randomly generate thirty birthdays. okay. I'm giving you some paper to do this on. first thing you're going to do, I've got the sheets to explain this in a second but I just thought I'd do it on the board quickly. is you're going to throw a coin and get a head or a tail and roll a dice. okay roll a dice. you'll get one to six? that is going to tell you the month that you're going to choose. so let's go that way. January February, March, April, May, June, July, August, September, October, November, December. so if you rolled a head and a four, then it would be July, the birthday would be in July. so it's a way of randomly generating the day
326 Teacher: okay
328 Teacher: excuse me. guys I'm not impressed. SNAME. the second time. the second time is just gonna be a double dice roll, I couldn't find enough, enough dice this morning to give you two each. a double dice roll, one to six obviously, you're going to have to roll it twice to get the date. one two three four etcetera all the way up to thirty-one. if you get, if you get one of these down here or if you get a date that doesn't exist then you just need to roll the dice again to generate another date. if you get like February the thirty first. obviously that doesn't exist? so you just roll, leave it as February, roll it again get another date. on. sh.
330 Teacher: sh. excuse me. guys. not impressed with the amount of actually shouting I've got to do today. on that sheet it explains it. okay. it's got the two tables for you. okay. you need to generate, so on a piece of paper you need to write one to thirty and write down thirty birthdays, randomly generated using this technique. okay. so make sure you've got a coin. if you've not got a coin see me. you've got about six minutes, well seven minutes to generate thirty random birthdays off you go
332 Teacher: gonna give you about five minutes.
334 Teacher: okay roll once more and then stop. I don't want to hear anybody rolling anything after one more roll each.
336 Teacher: guys. stop rolling. hurry up. stop. guys I don't want to hear the dice or the coins moving any more please. okay. you've had enough time to roll thirty. a lot of people did manage to roll their thirty. some of the people that took too long to get started maybe didn't. okay. but most people did get to roll thirty. on your list then. or if you've grouped it as a table, because. on your lists or if you've grouped it as a table. how many, who's actually got in their list two birthdays that are the same. okay. there's a few of you that have. now. okay. how. you've just got two the same.
338 Teacher: your first two were the same weren't they. yeah. June the twenty third for the first two. okay. what did you get as the same?
340 Teacher: September the twenty ninth.
342 Teacher: October twelfth. okay. it's quite possible that in a group of thirty you will have two birthdays the same. how likely do you think it is. what, if you gave me a percentage chance of a group of thirty people, having the same birthday what do you think it is. SNAME?
344 Teacher: about about
346 Teacher: eight to ten percent chance.
348 Teacher: two percent chance. okay going based on our experiment though. how many pairs, how many groups of people did we have. let's say, because some of you grouped together. let's say we have about twelve groups of people. one two three four at least four,
350 Teacher: yeah so it's getting, that's a third then yeah
353 Teacher: it's getting a lot
354 Teacher: yeah. okay. so it would be more likely than two percent wouldn't it really. it appears to be more likely than two percent. it would more likely maybe than eight to ten percent. right. let's look at one thing. okay. if I chose one person. okay. if I said I've got a class that's just got SNAME in.
357 Teacher: he said it. er no it wouldn't SNAME. it wouldn't. er you know class that just had SNAME in it, I had one person in it. what's the probability that my class don't share a birthday.
360 Teacher: hundred percent. okay. one you're happy, one we just call it one don't we when we're talking about fractions okay. chances that he doesn't share is one. what's the probability then, of two people, in my class, sharing a birthday.
363 Teacher: nought. okay. what you're actually doing
366 Teacher: if I've only just got SNAME
369 Teacher: what's the probability of two people in that class sharing.
372 Teacher: okay. just talking about you lot, I'm not talking about me. okay. right. I wanna just quickly go through this. okay we do one minus one and the chance is nought. okay imagine I had two people. whats the probability of them not sharing a birthday.
374 Teacher: right. pick a random date. probability, probability, SNAME what's your random date please
377 Teacher: first of October. the probability of my first person having that birthday what would it be.
379 Teacher: right then you don't know. what would the probability of that be.
381 Teacher: one over three hundred and sixty-five?
385 Teacher: okay. one over three hundred and sixty-five.
386 Teacher: yeah. okay. well actually no that way won't work. let's do it the other way. let's do it the other way. how many options? imagine I had two people, these two. if I want them not to share a birthday. how many options have I got for a birthday for SNAME. I've actually got the full choice. it doesn't actually matter. three hundred and sixty-six. out of three hundred and sixty-six. I'm taking into account that we, we could be January the twenty ninth
388 Teacher: I think you're late SNAME
390 Teacher: okay. say again. that's fine. how many options have I got for SNAME. if I don't want them to have the same birthday, how many options have I got.
393 Teacher: three hundred and sixty-five. so the probability of them not sharing a birthday is that. if I actually worked that out. okay. if I actually worked that out I get nought point, I've got a calculator but I'm just going to read it off this, nought point nine nine seven two. one minus that. is nought point nought nought two seven. okay now. if I had thirty people. I will have to do, not sharing, I would have to do. three hundred and sixty-six over three hundred and sixty-six times three hundred and sixty-five over three hundred and sixty-six times times three hundred and sixty four. all the way down thirty times. okay probability of that then. is that. so, in fact. for thirty people. for thirty people, let's just work it out. one minus nought point two nine seven four it's actually, what's that as a percentage? if that's a decimal what's that as a percentage.
395 Teacher: not seventy-five percent
397 Teacher: seventy point two six percent. so in fact. in a class of thirty people, there's just over a seventy percent chance that you share a birthday with somebody else. so it's not eight to ten SNAME. it's not two. it's actually seventy percent. is that a lot more than you think, thought it would be?
400 Teacher: does everybody thought it would be a lot lower than that.
404 Teacher: yeah?
407 Teacher: two people in that class sharing a birthday
409 Teacher: okay. what about then. what about. two people sharing a birthday, if I wanted them to get roughly fifty percent. how many people do you think you need in the class to have it at roughly a fifty fifty chance that they will share a birthday.
412 Teacher: it's a bit more than ten
414 Teacher: well no it's less than, we know it's less than thirty
417 Teacher: if you had a class of twenty-three people there's a just roughly a fifty fifty percent chance, fifty fifty chance that they will share the same birthday. you could work that out. every ((inaudible)) birthday. it would be a really big probability. okay. what I want you to do is pack away. stand behind your chairs. leave the stuff on the table. without rolling the dice anymore. pack away please
