For Cathy's birthday, her uncle decided to make her a deal. He took ten singles and ten one hundred dollar bills, and asked Cathy to divide them into two piles as she saw fit. He would then blindfold her, and thoroughly shuffle each pile of bills, so that the order was completely random. Finally, he would put each pile in a separate box.

Cathy is to pick one of the two boxes at random, and then pick out a random bill from that box (still blindfolded). She would get to keep whatever bill she pulls out.

Naturally, Cathy prefers to get a $100 bill. What strategy should she use in breaking up the bills into two piles to maximize her chance of getting a hundred?

Cathy should put one $100 in the first pile, and all $910 dollars of the rest in the second pile. When she picks her box, there will be a 50% chance that she will pick the lone $100 bill. If she picks the other pile, she has a 9 out of 19 chance (= 47.368%) of getting a $100 bill.

Altogether she has a (50% * 100%) + (50% * 47.368%) = 50% + 23.684% = 73.684% chance of getting $100.

Posted by TomM on 2002-05-28 07:01:26