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Math Help - 2D probability question..

  1. #1
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    2D probability question..

    in a jar we have 3 balls one red one white one black

    3 people choose a ball and return it back.

    x represents the number of different colors which the 3 people chose
    y represents the number of white balls chosen.

    p(x,y)
    find p(2,0)

    we have in total 27 possibilities
    3 people chose 2 different colors(from the existing 3) and non of them was white

    so each guy need to chose red or black out of 3 balls
    \binom{3}{1}+\binom{3}{1}

    why the answer is \frac{2\binom{3}{2}}{27}
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  2. #2
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    Quote Originally Posted by transgalactic View Post
    in a jar we have 3 balls one red one white one black

    3 people choose a ball and return it back.

    x represents the number of different colors which the 3 people chose
    y represents the number of white balls chosen.

    p(x,y)
    find p(2,0)

    we have in total 27 possibilities
    3 people chose 2 different colors(from the existing 3) and non of them was white

    so each guy need to chose red or black out of 3 balls
    \binom{3}{1}+\binom{3}{1}

    why the answer is \frac{2\binom{3}{2}}{27}
    Actually, the correct answer is \frac{2}{9}!

    Note that \binom{3}{2}= \binom{3}{1}= 3 so the only difference between your answer and the given answer is the "27" in the denominator. That is there, of course, because there are a total of 27 possible outcomes:
    \frac{\binom{3}{1}+ \binom{3}{1}}{27}= \frac{2\binom{3}{2}}{27}= \frac{(2)(3)}{27}= \frac{2}{9}.
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