A family decides to have children until it has three children of the same gender. Assuming P(B) = P(G) = .5, what is the pmf of X = the number of children in the family?

Answer : Step 1 : Given a family decides to have children until it has three children of the same gender. We assuming P(B) = P(G) = 0.5. Then we have to find the pmf of X = the number of children in the family. Here there are 3 of the same. So the probability they have 1 or 2 is zero in each case. Then unless there is a third sex which I haven't heard about. So they have not 6. Then the probability is 0. We consider 3 cases : P(3 children) , P(4 children) : P(5 children). Here B and G are students. So we have 2 children. 3 So 2 = 8 So the possibilities are : First is 3 children is So 2 = 8 Here total number of children is 8. = {GGG, GGB, GBG, BGG, GBB, BGB, BBG, BBB} = 2 8 1 = 4 = 0.25 Therefore the probability of three same-sex children4= Second...