Suppose P(A)= .3, P(B)=.4, and the P(A + B) = .12. What is:
a.) P(A/B)?
b.) P(B/A)?
c.) are A and B independent? Explain your answer.
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)