HMMT 十一月 2010 · GEN2 赛 · 第 8 题

HMMT November 2010 — GEN2 Round — Problem 8

[ 5 ] Allison has a coin which comes up heads of the time. She flips it 5 times. What is the probability 3 that she sees more heads than tails?

解析

[ 5 ] Allison has a coin which comes up heads of the time. She flips it 5 times. What is the probability 3 that she sees more heads than tails? 64 Answer: The probability of flipping more heads than tails is the probability of flipping 3 heads, 81 ( ) 5 2 1 n 5 − n 4 heads, or 5 heads. Since 5 flips will give n heads with probability ( ) ( ) , our answer is n 3 3 ( ) ( ) ( ) 5 5 5 2 3 1 2 2 4 1 1 2 5 1 0 64 ( ) ( ) + ( ) ( ) + ( ) ( ) = . 3 3 3 4 3 3 5 3 3 81