100 枚硬币正面数为奇数的概率

先抛前 99 枚。无论前 99 枚出现奇数还是偶数个正面，最后一枚硬币以 $1/2$ 概率把奇偶性翻转到“奇数”。

因此概率为 $\boxed{\tfrac{1}{2}}$。

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Original Explanation

Imagine flipping 99 coins first. The last coin always decides whether we observe an odd or even number of heads. Thus, the probability of observing an odd number of heads is $\frac{1}{2}$.