Solution to 8):

The answer to the first is 1/3, and to the second 1/2. The reason they are different is because in the first case the Smiths' statement changes the space over which you sample from {GG, GB, BG, BB} to {GG, GB, BG}. The chances of there being two girls is therefore 1/3.

If, on the other hand you meet the Smiths with a daughter of theirs, you are alrady sampling the distribution in {GG, GB, BG, BB}, thereby reducing the sample space to {GG, GB}. The probability is therefore 1/2 in this case.