What is the probability that a family of 4 would have exactly 2 girls and 2 boys?

For the sake of ease, I'm going to assume that you mean: if a family were to have four children, what is the probability of having two girls and two boys. (Note: if you actually mean a family of four, you would have to start building in the probability of single-parenthood and same-sex adoption since the parents would be included in the total family size.) One could do this problem the long way by writing out all combinations of children and identifying which one meets the criteria given in the problem and which ones do not. All Possible Combos of 4 Children GGGG BGGG GBGG GGBG GGGB BBGG BGBG BGGB GBGB GBBG GGBB GBBB BGBB BBGB BBBG BBBB Each set that matches our criteria are in bold. There are 6 "successful" pairings, out of a total of 16 possible combinations. Thus the probability is 6/16 or .375 or 37.5% that there will be two girls and two boys. That is a long way of doing this problem however and would not be as quick if we had asked about 10 children instead of only 4. Instead it is easier to think of this problem as the probability of one possible combination being correct then multiplying it by all the possible ways of writing it. You can take any possible combination of B and G as long as there are 2 Bs and 2 Gs. For this problem lets use: BBGG. The probability of this exact combination occurring is 1/16: (1/2) * (1/2) * (1/2) * (1/2) = 1/16 Remember that the probability of a certain series of independent events is equal to the each probability multiplied together. Now we must figure out all the possible ways of writing BBGG. In this case there are 6. So now 6 * (1/6) = 6/16 or 3/8 or .375 or 37.5%