5 次抛硬币恰好出现一段 3 连正面

恰好出现一段 HHH 的模式只能是：HHHT?、THHH T、?THHH（并且两侧不能再扩展成更长连串）。

计数可得共有 5 个符合序列，因此概率为

$$\frac{5}{2^5}=\frac{5}{32}.$$

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Original Explanation

Note that the sequence must be in the form $HHH--, -HHH-, --HHH$. For the first form, the first dash must be $T$ so that the run doesn't extend. The second dash can be anything, so this gives 2 options. For the second form, both dashes must be tails because the $HHH$ is adjacent to both dashes, so this is just one possibility. The last sequence must have a $T$ in the second dash so that the run doesn't extend. The first dash can be either outcome, so this gives 2 sequences as well. Therefore, we have 5 sequences corresponding to this outcome, so the probability is $\frac{5}{32}$.