stats homework please help

Question

Mike plays basketball and his stats say he has a 82% chance of making any free throw shot. When he gets to shoot more than one free throw his chance of making the second shot increases to 90% if he makes the first one. Suppose Mike just was fouled and is on the free throw line about to shoot 2 shots.

Calculate the probability that Mike:

(a) Makes both shots

(b)Only makes the first shot

(c) Misses both shots

Answer 1

A = make 1st shot

B = make 2nd shot

a)

P(A and B) = P(A) * P(B|A) = 0.82 * 0.9 = 0.738

b)

P(A) = P(A and B) + P(A and B')

P(A and B') = P(A) - P(A and B) = 0.82 - 0.738 = 0.082

c) P(A' and B') = P(A') * P(B'|A') = 0.2 * 0.2 = 0.04