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Math Help - One bag contains 4 white balls

  1. #1
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    One bag contains 4 white balls

    Question : One bag contains 4 white balls and 2 black balls; another contains 3 white balls and 5 black balls. If one ball is drawn from each bag, find the probability that (i) both are white , (ii) one is white and one is black.
    --------------------------------------------------------------------------------------------------------------------------

    Pr(X = white ball from bag 1) = \frac{4}{6}

    Pr(X = white ball from bag 2) = \frac{3}{8}
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  2. #2
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    Hello, zorro!

    One bag contains 4 white balls and 2 black balls.
    Another contains 3 white balls and 5 black balls.
    If one ball is drawn from each bag, find the probability that
    . . (a) both are white
    . . (b) one is white and one is black.

    We have: . \boxed{\begin{array}{c}\text{Bag 1} \\ \hline \text{4 White} \\ \text{2 Black} \end{array}} \qquad \boxed{\begin{array}{c}\text{Bag 2} \\ \hline \text{3 White} \\ \text{5 Black}\end{array}}


    (a) Both White.

    . . \begin{array}{ccc}P(\text{W from Bag 1}) &=& \dfrac{4}{6} \\ \\[-3mm] P(\text{W from Bag 2}) &=& \dfrac{3}{8} \end{array}

    Therefore: . P(\text{both W}) \:=\:\frac{4}{6}\cdot\frac{3}{8} \:=\:\frac{1}{4}



    (b) one W, one B

    There are two scenariors:

    . . [1] W from Bag 1, B from Bag 2: . \frac{4}{6}\cdot\frac{5}{8} \:=\:\frac{20}{48}

    . . [2] B from Bag 1, W from Bag 2: . \frac{2}{6}\cdot\frac{3}{8} \:=\:\frac{6}{48}


    Therefore: . P(\text{one W, one B}) \:=\:\frac{20}{48} + \frac{6}{48} \:=\:\frac{26}{48} \:=\:\frac{13}{24}

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  3. #3
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    Quote Originally Posted by zorro View Post
    Question : One bag contains 4 white balls and 2 black balls; another contains 3 white balls and 5 black balls. If one ball is drawn from each bag, find the probability that (i) both are white , (ii) one is white and one is black.
    --------------------------------------------------------------------------------------------------------------------------

    Pr(X = white ball from bag 1) = \frac{4}{6}

    Pr(X = white ball from bag 2) = \frac{3}{8}
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