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Math Help - Marbles in Bags

  1. #1
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    Marbles in Bags

    Bag A contains 3 black marbles and 1 white marble and Bag B contains 1 black marble and 3 white marbles. If two marbles are randomly taken from Bag A and placed in Bag B, then a marble is randomly selected from Bag B, what is the probability that the marble selected from Bag B is black?

    I've tried to draw a tree, but I must be doing something wrong cause I can't get the correct answer. Could someone give me some guidance?
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  2. #2
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    Hello mneox
    Quote Originally Posted by mneox View Post
    Bag A contains 3 black marbles and 1 white marble and Bag B contains 1 black marble and 3 white marbles. If two marbles are randomly taken from Bag A and placed in Bag B, then a marble is randomly selected from Bag B, what is the probability that the marble selected from Bag B is black?

    I've tried to draw a tree, but I must be doing something wrong cause I can't get the correct answer. Could someone give me some guidance?
    The number of ways of selecting 2 marbles from the four in bag A is \binom42=6.

    The number of ways of selecting the white marble and one of the black marbles from bag A = 3.

    Therefore the probability that one of the marbles chosen from bag A is white is \tfrac36 = \tfrac12; and the probability that both are black is also \tfrac12.

    So, when a marble is drawn from bag B, half the time it will be chosen from a total of 2 black and 4 white, and half the time from 3 black and 3 white. So the probability that it is black is
    \frac12\times \frac26 + \frac12\times \frac36 = \frac{5}{12}
    Grandad
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