Question

Box A contains six white marbles and five black marbles. Box B contains three white marbles and four 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

We have four possible outcomes:
1 ww **
2 wb
3 bw
4 bb

we want the cases marked by **
#1:
ww, prob(first w) = 6/11
so the white gets transferred to B and
prob(2nd w) = 4/8 = 1/2
prob(ww) = (6/11)(1/2) = 6/22 = 3/11

Answer 2

well,
P(BW) = 5/11 * 3/8
P(WW) = 6/11 * 4/8

so, what does hat tell you?