SOLUTION: Let P(A) = 0.4 and P(A u B) 0.6: A) For what value of P(B) are A and B mutually exclusive? B) For what value of P(B) are A and B independent?

          Part (a) solution


Events A and B are mutually exclusive if and only if  P(A U B) = P(A) + P(B).

In our case, it should be

         0.6 = 0.4 + P(B),

which gives  P(B) = 0.6 - 0.4 = 0.2.


ANSWER.  P(B) = 0.2.


          Part (b) solution


We have a general formula P(A U B) = P(A) + P(B) - P(A n B), which is valid for all events A and B.

If A and B are independent, then  P(A n B) = P(A)*P(B).

So, in our case should be

    0.6 = 0.4 + P(B) - 0.4*P(B),

which implies

    0.6 - 0.4 = 0.6*P(B)

       0.2    = 0.6*P(B)

       P(B) =  = .


ANSWER.  P(B) should be .