Question

Box A contains 3 white marbles and 4 black marbles. Box B contains 6 white marbles and 5 black marbles. An experiment consists of first selecting a marble at random from Box A. The marble is transferred to Box B and then a second marble is drawn from Box B. What is the probability that the first marble was white given that the second marble was white?

Answer 1

prob(W from boxA) = 3/7

now we transfer a ball

case1, ball transferred is W
now we have 7white in B
prob(W from boxB) = 7/12

prob as stated = (3/7)(7/12) = 1/4

case 2, ball transferred is B
now we still have 6 W in B
prob(W from B) = 3/7 x 6/12 = 3/14

prob(of our event) = 1/4 + 3/14 = 13/28