Returning Homework and ProbabilityDate: 12/11/98 at 15:13:40 From: Adam Bergman Subject: Probability I'm passing back 25 papers to my 4th grade math challenge class. It's the homework that they just brought me, and I decided that we would grade each other's papers. One of the students raised her hand and said, "What if we get our own paper back?" I offer extra credit to anyone who does, since I am passing them out completely randomly. Another child says "Hey, that's not fair. The kids at the end have less chance of getting their own papers back." Another shouts "No, it's the other way around. The people at the beginning have less chance of winning!" I say "No, everyone has a 1/25 chance of getting his or her own paper back." The only thing is that I cannot explain why. The first one is easy. One winner out of 25 possibilities. But, how about the others? Date: 12/11/98 at 18:06:58 From: Doctor Anthony Subject: Re: Probability The chance that the first child will get the correct paper is as you say: 1/25. For the second child there are 24 papers, so the chance of getting the correct one is: first child correct, second child correct + first child incorrect (but not second child's paper), second child correct. So the probability is: Prob = 1/25 x 1/24 + 23/25 x 1/24 = (1/25)[1/24 + 23/24] = (1/25)[1] = 1/25 and so on. An easier explanation is as follows. There is no change to the probability situation if all the papers are placed round a table face down. All the children take up positions round the table at random. There is no reason for any child to be favoured in any way in this scenario. Finally, all together they turn over the paper in front of them. They all have the same chance that they have their own paper. - Doctor Anthony, The Math Forum http://mathforum.org/dr.math/ |
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