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

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Intern
Joined: 09 Aug 2006
Posts: 13
Q. Box A contains 3 red and 2 white marbles. Box B contains  [#permalink]

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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.
Senior Manager
Joined: 05 Mar 2006
Posts: 313
Re: Q. Box A contains 3 red and 2 white marbles. Box B contains  [#permalink]

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16 Aug 2006, 11:22
OK, here's a start:

For the Red:

A -> B = 3/5
B -> A = 3/8
Total probability = (3/5)(3/8) = 9/40

B -> A = 2/7
A -> B = 4/6 - 2/3
Total probability = (2/7)(2/3) = 4/21

For the White:

A -> B = 2/5
B -> A = 6/8 - 3/4
Total probability = (2/5)(3/4) = 3/10

B -> A = 5/7
A -> B = 3/6 - 1/2
Total probability = (5/7)(1/2) = 4/14

Not sure, what to do next?

(9/40)+(4/21)+(3/10)+(4/14)
Manager
Joined: 19 Jul 2006
Posts: 235
Re: Q. Box A contains 3 red and 2 white marbles. Box B contains  [#permalink]

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17 Aug 2006, 03:52
Box A Red marble = (1/2)*(3/5)*(3/8) = (1/2)*(9/40)
Box A White marble = (1/2)*(2/5)*(6/8)= (1/2)*(12/40)

Box B Red marble = (1/2)*(2/7)*(4/6)= (1/2)*(8/42)
Box B White marble = (1/2)*(5/7)*(3/6)= (1/2)*(15/42)

prob.= (1/2)*(9/40) + (1/2)*(12/40) + (1/2)*(8/42) + (1/2)*(15/42)
Director
Joined: 02 Jun 2006
Posts: 852
Q. Box A contains 3 red and 2 white marbles. Box B contains  [#permalink]

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17 Aug 2006, 07:58
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.

Prob(Success) = P(Ba)x [P(Wa)xP(Wb') +P(Ra)xP(Rb')] +
P(Bb)x[P(Wb)xP(Wa') + P(Rb)xP(Ra')]

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
Q. Box A contains 3 red and 2 white marbles. Box B contains   [#permalink] 17 Aug 2006, 07:58