Please see 2 images attached. Thank you!!!!

1. (10 points) X is a geometric random variable. Show that P(X 2 s+t|X 2 t) = P(X > s) .2. (10 points) Consider a family with two children. Assume that each child is as likely to be a boy as it is to be girl. What is the conditional probability that both children are boys, given that at least one of the children is a boy