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Q. Box A contains 3 red and 2 white marbles. Box B contains [#permalink]
16 Aug 2006, 11:01

Q. Box A contains 3 red and 2 white marbles.
Box B contains 2 red and 5 white marbles.

A box is selected at random; a marble is drawn and put into the other box; than a marble is drawn from the second box. Find the probability that both marbles drawn are of the same colour.

Long one so bear with me...
If Ba = Event of Box a being choosen
If Bb = Event of Box b being choosen
If Wa = Event of white ball being choosen from box A
If Wb' = Event of white ball being choosen from box B, after a white is picked from A and put in B

Define corresponding events for Red ball from box A, box A, and the events from Box B.

P(Ba) = P(Bb) = 1/2
P(Wa) = 2/5
P(Ra) = 3/5
P(Wa') = 3/6 {After white picked from B and put in A}
P(Ra') = 4/6 {After red picked from B and put in A}
P(Wb) = 5/7
P(Rb) = 2/7
P(Wb') = 6/8 {After white picked from A and put in B}
P(Rb') = 3/8 {After red picked from A and put in B}

Solving using above equations and values
P(Success) = 3604/6720 = 0.54