Problem 76 Solution

The probability of event A happening given that event B already happened is the probability of A and B happening divided by the probability that B happened. This can be pressed as Pr(A|B)=Pr(A and B)/Pr(B).

In this case A is drawing a black marble and B is having already drawn a black marble.

Pr(A and B) = (1/2) * [(3/4)2 + (1/4)2] = 5/16.

Pr(B) = 1/2.

Pr(A|B) = Pr(A and B)/Pr(B) = (5/16)/(1/2) = 10/16 = 5/8.

Michael Shackleford, A.S.A.