PA and B 2 PB 6 and PA and B 1 Are events A and B indepen

P(A’ and B’) = .2, P(B) = .6, and P(A and B) = .1. Are events A and B independent?

Solution

If A and B are independent, then

P(A) P(B) = P(A and B)

As

P(A\' and B\') = 0.2

Then

P(A U B) = 1 - P(A\' and B\') = 1 - 0.2 = 0.8

Hence,

P(A) + P(B) - P(A and B) = 0.8

P(A) + 0.6 - 0.1 = 0.8

P(A) = 0.3

Hence,

P(A) P(B) = 0.3*0.6 = 0.18

P(A and B) = 0.1

As they are not equal, NO, THEY ARE NOT INDEPENDENT. [ANSWER]