HMMT 二月 2015 · COMB 赛 · 第 9 题

英文解析

9. Calvin has a bag containing 50 red balls, 50 blue balls, and 30 yellow balls. Given that after pullingout 65 balls at random (without replacement), he has pulled out 5 more red balls than blue balls, whatis the probability that the next ball he pulls out is red?
   Answer: Solution 1. The only information this gives us about the number of yellow balls 9
   left is that it is even. A bijection shows that the probability that there are k yellow balls left is equal 26
   to the probability that there are 30 − k yellow balls left (flip the colors of the red and blue balls, andthen switch the 65 balls that have been picked with the 65 balls that have not been picked). So theexpected number of yellow balls left is 15. Therefore the expected number of red balls left is 22 . 5. So