HMMT 十一月 2010 · GEN2 赛 · 第 8 题

英文解析

8. [ 5 ] Allison has a coin which comes up heads of the time. She flips it 5 times. What is the probabilitythat she sees more heads than tails?3
   Answer: The probability of flipping more heads than tails is the probability of flipping 3 heads,64
   ( )81
   2 15
   n 5 − n
   4 heads, or 5 heads. Since 5 flips will give n heads with probability ( ) ( ) , our answer isn 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