HMMT 十一月 2016 · 冲刺赛 · 第 1 题

1. [ 5 ] If five fair coins are flipped simultaneously, what is the probability that at least three of them show heads? Proposed by: Allen Liu 1 Answer: 2 The coin either lands heads-up at least three times or lands heads-down at least three times. These 1 scenarios are symmetric so the probably is just . 2 5 5 5

( ) ( ) ( ) 3 4 5 16 1 Alternatively, we can explicitly compute the probability, which is just = = 5 2 32 2 10