3 child family.... probability that all three children are girls given that at least one of the kids is a girl?
P(E) = all 3 kids are girls. P(F) = at least one is a girl. Total # of outcomes: {GGG, GGB, BBB, BGG, BGB, GBG, GGB, BBG} 8 outcomes total. P(E) = {GGG} P(F) = {BBG,GBB,BGB,GGG} so I think I must use P(EintersectF)/ P(E).
Yes, you are on the right track. To find the probability that all three children are girls given that at least one is a girl, you can indeed use the formula P(E ∩ F) / P(F).
First, let's find P(F), which is the probability that at least one of the children is a girl. There are three outcomes where at least one child is a girl: {GGG, GGB, GBG}. So P(F) = 3/8.
Next, we need to find P(E ∩ F), which is the probability that both events E (all three children are girls) and F (at least one child is a girl) occur together. Since event E is a subset of F (every outcome in E is also in F), we know that P(E ∩ F) = P(E). So P(E ∩ F) = 1/8.
Finally, we can find P(E), the probability that all three children are girls. As you correctly identified, there is only one outcome where all three children are girls: {GGG}. So P(E) = 1/8.
Now, we can calculate the probability that all three children are girls given that at least one is a girl using the formula P(E ∩ F) / P(F):
(P(E ∩ F)) / P(F) = (1/8) / (3/8) = 1/3
Therefore, the probability that all three children are girls given that at least one is a girl is 1/3.