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Math Help - probability of picking coloured balls

  1. #1
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    probability of picking coloured balls

    A bag X contain 5 black balls and 3 white balls. A bag Y contains 4 black balls and 7 white balls. A ball is picked randomly from bag X and placed into bag Y. A ball is picked randomly from bag Y. Find the probability of the ball picked from bag Y is white.

    the ans is 59/96. how do do this?
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  2. #2
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    Re: probability of picking coloured balls

    there are two ways this can happen

    a) you pick a black ball from X and pick a white ball from Y

    b) you pick a white ball from X and pick a white ball from Y

    in (a)

    A black ball is picked from bag X with probability 5/8.

    bag Y then has 5 black balls and 7 white balls when the pick is made. Thus the probability of picking a white ball is 7/12.

    The probability of this chain is thus 5/8 * 7/12 = 35/96


    in (b)

    A white ball is picked from bag X with probability 3/8

    bag Y then has 4 black balls and 8 white balls. Thus the probability of picking a white ball is 7/12

    The probability of this chain is thus 3/8 * 8/12 = 24/96

    The overall probability of picking a white ball from bag Y is the sum of these two, i.e.

    (35+24)/96 = 59/96
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