Children and Daughters

Here are two interesting problems for you.

Problem 1:

I have 100 children. The oldest 99 are girls. What is the chance that I have 100 daughters?

Show Answer

The answer is 1/2. Quite obvious, really.

Simple, no? Now for the next problem.

Problem 2:

I have 100 children. At least 99 of them are girls. What is the chance that I have 100 daughters?

Show Hint 1

No, the answer is not 1/2. Try again.

Show Hint 2

Use conditional probability to solve the problem.

Show Answer

The answer is 1/101. Compute this by finding P(A|B), where event A is having 100 daughters, and event B is having at least 99 daughters.

A fun problem, though I didn't really get it right instantly too.