Question 1026448
Now P(P) = probability that “the sum shown is 8” = 5/36, and 
P(Q) = probability that “the two dice show the same number” = 6/36 = 1/6.

==>P(P|Q) = P(P∩Q)/P(Q) = {{{(1/36)/(1/6) = 1/6}}}.
Also, P(Q|P) =  P(P∩Q)/P(P) = {{{(1/36)/(5/36) = 1/5}}}.

Note:  P(P∩Q) = 1/36 because only the outcome (4,4) will satisfy the event P∩Q.