Question: Probability question

My question is concerning finding Px(k) for a problem. There is a basketball player who takes two foul shots. The P of making the first is 2/3. Then assuming she missed the first, the P of making the second is 3/4, but if she makes the first, P of making the second shot is 1/2. X is the number of shots made. I have to find Px(k) for k=0,1,2, and then E(X). My first concern and real problem is that I'm not sure how to find Px(k) for one shot made since the probabilities for making one shot have two possible answers. Do you average the probability for making the first shot and missing the second with the probability of missing the first and making the second?

Please Wait...