Calculate the probability that a family of 3 children has:
- Exactly 2 boys
There are a total of 8 outcomes (B for boy, G for girl):
Out of these there are 3 outcomes (#2, #3 and #5) that have exactly 2 boys so the probability is \(\frac{3}{8}\)
- At least 2 boys
It’s enough to add one outcome (all boys) to the result in a) to get 4 outcomes with the final probability of \(\frac{4}{8} = \frac{1}{2}\)
- At least 1 boy and at least 1 girl
We can exclude the 2 outcomes that have only boys (#1) or only girls (#8), for the total of 6 outcomes which gets us the probability of \(\frac{6}{8} = \frac{3}{4}\)