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Math Help - probability of colours of balls

  1. #1
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    Apr 2009
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    Smile probability of colours of balls

    the question is :

    (b) Box 1 contains six red balls and four green balls and box 2 contains seven red balls and three green balls. A ball is chosen at random from box 1 and placed in box 2. A ball is then chosen at random from box 2 and placed in box 1.

    Calculate
    (i) the probability that a red ball is selected from both box 1 and box 2;

    (ii) the probability that, at the conclusion of the selection process, there are again six red balls and four green balls in box 1.

    thanks
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  2. #2
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    Oct 2008
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    Quote Originally Posted by master_2m8 View Post
    the question is :

    (b) Box 1 contains six red balls and four green balls and box 2 contains seven red balls and three green balls. A ball is chosen at random from box 1 and placed in box 2. A ball is then chosen at random from box 2 and placed in box 1.

    Calculate
    (i) the probability that a red ball is selected from both box 1 and box 2;

    (ii) the probability that, at the conclusion of the selection process, there are again six red balls and four green balls in box 1.

    thanks
    Hi,

    i) P(\text{red in box 1})=\frac{6}{10}
    I assume that the red ball is placed in box 2 now:
    P(\text{red in box 2})=\frac{8}{11}
    P(\text{red from box 1 and 2})=(\frac{6}{10})(\frac{8}{11})

    ii) We can look at two cases when red ball is transfered and green ball is transfered:
    P(\text{6 red and 4 green in box 1 after transfer})= (\frac{6}{10})(\frac{8}{11})+(\frac{4}{10})(\frac{  4}{11})
    Last edited by noob mathematician; May 24th 2009 at 08:50 PM.
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  3. #3
    Junior Member
    Joined
    May 2009
    Posts
    39

    colour of ball

    a) Pr( red in the first time and red in the second) = Pr(red in the first). Pr(red in the second | red in the first) (conditional probability)

    = 6/10 . 8/11 = 24/55
    b) A: the event red in the first and red in the second moving .
    Ag: the event green in the first moving and green in the second
    B: the event that after 2 moving there are again 6 red and 4 green in the box 1. We need calculate Pr(A|B) = ?
    Pr(A|B) = Pr(AB)/ Pr(B) = Pr(A)/Pr(B) (because A \subset B)

    We calculate Pr(B):
    Pr(B) = Pr(A) + Pr(Ag) --> the result
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