4.4 Exercise 13

A basketball player takes ten free throws in a contest. On her first shot she is nervous and has probability 0.3 of making the shot. She begins to settle down and probabilities on the next seven shots are 0.5, 0.6 0.7 0.8 0.8, 0.8 and 0.85, respectively. Then she realizes her opponent is doing well, and becomes tense as she takes the last two shots, with probabilities reduced to 0.75, 0.65. Assuming independence between the shots, what is the probability she will make k or more for $k = 2 , 3 , \hdots 10 ?$