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Math Help - Probability

  1. #1
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    Probability

    Hi everyone,

    I really need an urgent help with the task below!!!
    PLEASE HELP!!! I'D REALLY APPRECIATE IF YOU COULD HELP ME WITH IT.

    An urn contains 10 balls: 4 red and 6 blue. A second urn contains 16 red balls and an unknown number of blue balls. A single ball is drawn from each urn. The probability that both balls are the same colour is 0.44.
    Calculate the number of blue balls in the second urn.



    THANKS IN ADVANCE
    Last edited by kochwow; March 24th 2009 at 01:17 PM.
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  2. #2
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    \frac{6}{10}\cdot \frac{b}{(16+b)} + \frac{4}{10}\cdot \frac{16}{(16+b)} = 0.44
    Solve for b.
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  3. #3
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    Quote Originally Posted by kochwow View Post
    An urn contains 10 balls: 4 red and 6 blue. A second urn contains 16 red balls and an unknown number of blue balls. A single ball is drawn from each urn. The probability that both balls are the same colour is 0.44.
    Calculate the number of blue balls in the second urn.
    Let N be the number of blue balls in the second urn. The probability that the first ball drawn is red is 2/5. The probability that the second ball is also red is 16/(16+N) so the probability both balls are red is (2/5)(16/(16+N)).

    The probability that the first ball is blue is 3/5 and the probability that the second ball is blue is N/(16+N) so the probability that both balls are blue is (3/5)(N/(16+N)).

    The probability that the two balls are the same, then, is (2/5)(16/(16+N))+ (3/5)(N/(16+N)). To find N, solve (2/5)(16/(16+N))+ (3/5)(N/(16+N))= 0.44 for N.
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