A man fires 8 shots at a target. Assume that the shots are independent, and each shot hits the bull's eye with probability 0.7.
a) What is the chance that he hits the bull's eye exactly 4 times?
b) Given that he hit the bull's eye at least twice, what is the chance that he hit the bull's eye exactly 4 times?
c) Given that the first two shots hit the bull's eye, what is the chance that he hits the bull's eye exactly 4 times in the 8 shots?