A coin is tossed three times. What is the probability that exactly two heads occur, given that

(a) the first outcome was a head?

(b) the first outcome was a tail?

(c) the first two outcomes were heads?

(d) the first two outcomes were tails?

(e) the first outcome was a head and the third outcome was a head?

I need to get a solution with a sample space and probability formula explaining the problem please.