Find the conditional probability of the indicated event when

Find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled.

The sum is 7, given that the green one is either 3 or 6.

Solution

Sum= G+Y

P(sum =7/ G= 3U6) P(G=3U6) = P(Y=4 and G=3 ; Y=1 and G=6)

P(sum =7/ G= 3U6) (2/6) = 2/36

P(sum =7/ G= 3U6)= (2/36 ) /(2/6) = 1/6