HMMT 二月 2004 · GEN2 赛 · 第 2 题
HMMT February 2004 — GEN2 Round — Problem 2
题目详情
英文原题
- 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
英文解析
- 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 shemust flip two heads immediately at the beginning. This happens with probability .1 4