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Math Help - conditional probabiklity

  1. #1
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    conditional probabiklity

    Box A contains 3 black balls and a white balls .Box B has 2 black balls and 3 white balls . The probability of chossing box A and B are 2/3 and 1/3 respectively . After the box is chosen , a ball is withdrawn from the box . If theball drawn is black , what is the probability that it was taken from box B ?

    P(B | Bl)=P(Bl n B)/P(Bl)=(1/3 x 2/5)/(5/9)=6/25

    but the answer given is 4/19 , could someone point me to my mistake ?
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  2. #2
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    P(B | black) = (1/3 * 2/5) / [(2/3 * 3/4) + (1/3 * 2/5)]
    =4/19
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  3. #3
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    Quote Originally Posted by mehn View Post
    P(B | black) = (1/3 * 2/5) / [(2/3 * 3/4) + (1/3 * 2/5)]
    =4/19
    thank you !
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