HMMT 二月 2004 · GEN2 赛 · 第 2 题
HMMT February 2004 — GEN2 Round — Problem 2
题目详情
- Andrea flips a fair coin repeatedly, continuing until she either flips two heads in a row (the sequence HH ) or flips tails followed by heads (the sequence T H ). What is the probability that she will stop after flipping HH ?
解析
- Andrea flips a fair coin repeatedly, continuing until she either flips two heads in a row (the sequence HH ) or flips tails followed by heads (the sequence T H ). What is the probability that she will stop after flipping HH ? Solution: 1 / 4 The only way that Andrea can ever flip HH is if she never flips T , in which case she 1 must flip two heads immediately at the beginning. This happens with probability . 4