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Current time:0:00Total duration:6:59

Video transcript

a magician performing at a birthday party stands inside a circle of 15 kids he's going to choose a volunteer and he wants each kid to have the same chance of getting chosen fair enough now we have three methods by which he can do it and let's just think about whether each of these methods are fair where each kid does have where each kid does have the same chance of getting chosen and if they're not if they don't lead to each kid having the same chance of getting chosen think about why that is the case so method one the magician starts with the birthday boy and moves clockwise passing out 100 pieces of paper numbered 1 through 100 he cycles around the circle until all the pieces are distributed he then uses a random number generator to pick an integer 1 through 100 and chooses the volunteer with that number so let's just think about what's happening so there's 15 kids in a circle so there's 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 I planned that out amazingly well I didn't think out if you'll be able to fit exactly 15 but it worked out so 15 kids in a circle and then he's going to hand out pieces of paper so he's going to he's going to let's give 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 and now this person is going to get pieces of paper 1 and 16 now this is going to get 2 and 17 you're going to keep going around and round and round until all hundreds all hundred pieces of paper are going to get distributed now something to think about is whether every student every Stewie every child here is going to get the same number of pieces of paper I encourage you to pause this video and think about that if we just keep cycling around all the way to 100 does each child get the same number of pieces of paper well just think about it in order to get the same number of pieces of paper 100 has to be divisible by 15 and we know 100 isn't is visible by 15 15 goes into 100 6 times 6 times 15 is 90 and you have a remainder of 10 so what's going to happen is all 15 kids are going to get 6 pieces of paper and then another 10 of the 15 are going to get a seventh piece of paper so they're not all getting an equal number of pieces of paper so even though he's randomly picking an integer between 1 and 100 some of the students are going to have a higher chance and the other ones the 10 that have 7 pieces of paper are going to have a higher chance than the other 5 who only have 6 pieces who only have 6 pieces of paper and so I would say method 1 a method 1 is not fair let me write this down not not fair sometimes life isn't fair but in this in this case it's not fair where we define fair is the same chance of getting chosen and that's because they don't have all have well they all they all have different numbers of pieces of paper they're not all of the students are not equally likely to get picked let's look at method 2 the magician starts with the birthday boy and moves around and moves counterclockwise passing up 75 pieces of paper numbered 1 through 75 he cycles around the circle until all the pieces are distributed he then uses a random number generator to pick an integer between 1 through 75 and chooses the volunteer with that number so encourage you to pause this video and think about whether this one method to whether that one is fair well method two is the same as method one except for instead of using 100 pieces of paper we're using 75 pieces of paper and so we have to think about is 75 divisible by 15 and 75 is 5 times 15 is 75 so in this situation each student is going to get 5 pieces of paper each gets 5 pieces of paper so they all have an equally likely chance of getting picked and then he's using a random number generator picked them so they all have an equally likely chance I would say method 2 is method 2 is indeed is indeed fair they all have an the same chance of getting chosen now let's think about method 3 method 3 the magician starts with the fit with the birthday boy and moves clockwise passing out 30 pieces of paper numbered 1 through 30 so they're all going to get the same number of pieces of paper they're all going to get two pieces of paper each 15 children getting 2 pieces of paper each would be 30 pieces of paper so that looks reasonable so far he cycles around the circle until all the pieces are distributed here so everyone gets two pieces he gives number one of the birth to point number two the next kid and so on so that all seems reasonable kind of consistent with method two except not instead of seventy-five it's 30 and obviously 75 was overkill he could even hear this is overkill he just really needs 15 pieces of paper and he then counts the number of windows in the room and chooses the volunteer with that number so the question here is is the number of windows in the room is it random and is it evenly distributed so maybe maybe you could make a case depending on what building it's in in someone's house it's somewhat random on how many video many how many windows that house happens to have the house that's happening to host the birthday party but it's not going to be evenly it's not going to be evenly distributed most III don't know they're just probably there's probably you know there's probably some if you were to sit and plot all of the houses that had a birthday party you'd probably see this more likely that I know that they have ten windows than one window or it's more and definitely more likely that they have ten windows and then let's say then then thirty windows or even maybe fifteen windows even and so it's not going to be evenly distributed this really isn't a this this is you know every house I guess has a somewhat different number of windows and and the house that is happening to host the party is seems to be somewhat random but it's not going to be evenly distributed here and I would say it's not a kind of a a really good random number generator because it's not evenly generated and so I would say method three is not fair not fair the number of windows is not a really good random number generator random - good enough a random number generator we would want say a number one through 75 where any of these have an equally likely chance of getting picked this is it's somewhat random the number of windows that that building has but it's it's they're not all equally equally likely