Suppose that we have two events, A and B, with P(A) = 0.50, P(B) = 0.60, and P(A ∩ B) = 0.05. If needed, round your answer to three decimal digits.
(a) Find P(A | B).
(b) Find P(B | A).
(c) Are A and B independent? Why or why not? A and B _____ independent, because _____ P(A).
Solution:
a)
P(A | B) = P(A B ) / P(B)
= 0.05 / 0.60
= 0.083
b)
P(B | A) = P(A B ) / P(A)
= 0.05 / 0.50
= 0.100
c)
P(A B ) = P(A) * P(B)
= 0.50 * 0.60
= 0.300
A and B are not independent, because the probability of A and B is not same.
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