Ten fair coins are flipped. Given that there are at least nine heads, what is the probability that all the coins show heads?
The answer is $\frac{1}{11}$. Among the $2^{10}=1024$ sequences of heads and tails, note that

- There is only 1 which is all heads, and
- There are 10 sequences which have exactly one tails.

So there are 11 possible sequences with at least nine heads, only one of which is all heads. Hence the answer is $\frac{1}{11}$.