Problem 77 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 Pr(A and B) = 5*(The integral from 0.4 to 0.6 of p²) =

5*(p³/3 from 0.4 to 0.6) =

(5/3)*(.216 - .064) =

19/75 =~ 0.2533333

Pr(B) = 5 * The integral from 0.4 to 0.6 of p = 0.5 .

Thus the answer is 38/75 =~ .5066667

Michael Shackleford, A.S.A.