Events A and B in a sample space have P(A) = 1 4 , P(B) = 1 3 and P(A ∪ B) = 17 36 . (i) Find P(A ∩ B). (ii) Find P(A|B)

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Events A and B in a sample space have P(A) = 1 4 , P(B) = 1 3
and P(A ∪ B) = 17 36 . (i) Find P(A ∩ B). (ii) Find P(A|B). (iii)
Find P(B|A). (iv) Are A and B independent? Why or why
not?
(b) The probability that a certain beginner at golf gets a good
shot if he uses the correct club is 1 3 , and the probability of a
good shot with an incorrect club is 1 4 . In his bag are 5
different clubs, only one of which is correct for the shot in
question. If he chooses a club at random and takes a stroke, what
is the probability that he gets a good shot?
(c) In part (b), if it is known that a good shot has resulted,
what is the probability that the right club was used?