概率2连续3个硬币翻转，甚至头部

Question

我遇到了这个问题。考虑到头部数量是均匀的，你在3次硬币翻转中连续获得2个头的概率是多少。

My Attempt:
Sample Space: {HHH, HHT, HTT, HTH, THH, TTH, THT, TTT}
Event F is even number of heads from 3 flips: {HHT, HTH, THH}
P(F)= 1/8 + 1/8 + 1/8 = 3/8
Event E is 2 heads in a row given F:
{HHT, THH}
P(EnF)= 1/8 + 1/8 = 2/8 = 1/4

Probability of E given F = P(EnF)/P(F)
(1/4) / (3/8)= 2/3

然而，书的后面说E的概率给定F = 1/2

我做错了什么？

Answer 1

TTT也算作偶数H的结果。