Suppose P(A)= .3, P(B)=.4, and the P(A + B) = .12. What is:

Question

a.) P(A/B)?

b.) P(B/A)?

c.) are A and B independent? Explain your answer.

Answer 1

P(A/B) is the probability of A when B also happens. It equals 0.12/0.4 = 0.3, which is also P(A)

P(B/A) is the probability of B if A also happens. It equals 0.12/0.3 = 0.4, which also equals P(B)

The probability of A does not depend upon what happened to B and vice versa.

They are therefore independent.

This also follows from
P(A+B) = P(A)*P(B)