Probability and Events

Question

Events A and B are associated with the following probabilities.

P(A)=1/2

P(B)=1/3

P(B|A)=1/6

Are the events A and B dependent or independent and why?

Answers:

Events A and B are independent, because P(A)=P(B|A)

Events A and B are dependent, because P(A) does not equal P(B|A)

Events A and B are dependent, because P(B) does not equal P(B|A)

Answer 1

P(B|A)=P(A∩B)/P(A)

In this problem: 1/6 = P(A∩B)/(1/2), i.e. P(A∩B) = 1/12

If A and B are independent P(A∩B)=P(A)*P(B)

In this problem P(A)*P(B)=(1/2)*(1/3)

Since the 2 values calculated for P(A∩B) are not equal, the events are not independent.