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Probability Problem

  1. Jul 22, 2014 #1
    An urn contains 10 white and 3 black balls. Another urn contains 3 white and 5 black balls. 2 balls are drawn at random from the first urn and placed in the second urn and 1 ball is drawn at random from the second urn. What is the probability that it is white?

    Is the answer 59/130
     
  2. jcsd
  3. Jul 22, 2014 #2

    micromass

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    Please tell us why you think that.
     
  4. Jul 22, 2014 #3
    Check your arithmetic debdut.
     
  5. Jul 22, 2014 #4

    Ray Vickson

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    I also get 59/130. Nevertheless, the OP should show his/her work.
     
  6. Jul 22, 2014 #5
    I don't know whether I have done it correctly or not...

    There are 4 combinations of picking 2 balls from 1st urn (White → W, Black → B)

    WW → P = 10/13 x 9/12 = 15/26
    BB → P = 3/13 x 2/12 = 1/26
    WB → P = 10/13 x 3/12 = 5/26
    BW → P = 3/13 x 10/12 = 5/26

    If WW was picked, then balls in 2nd urn = 5W 5B, Then probability of picking white ball = 5/10
    If BB was picked, then balls in 2nd urn = 3W 7B, Then probability of picking white ball = 3/10
    If WB was picked, then balls in 2nd urn = 4W 6B, Then probability of picking white ball = 4/10
    If BW was picked, then balls in 2nd urn = 4W 6B, Then probability of picking white ball = 4/10

    Thus total probability of picking white ball from 2nd urn = (5/10 x 15/26)+(3/10 x 1/26)+(4/10 x 5/26)+(4/10 x 5/26) = 59/130
     
  7. Jul 23, 2014 #6

    HallsofIvy

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    Yes, that is correct.
     
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