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Math Help - drawing marbles from a bag

  1. #1
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    drawing marbles from a bag

    if there are 20 white marbles and 32 black marbles in a bag
    what is the probability of drawing 20 marbles where 10 are white and 10 are black ?
    is there a formula ?
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  2. #2
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    Quote Originally Posted by addison View Post
    if there are 20 white marbles and 32 black marbles in a bag
    what is the probability of drawing 20 marbles where 10 are white and 10 are black ?
    is there a formula ?
    Yes. Read this: Hypergeometric distribution - Wikipedia, the free encyclopedia.

    In your case: N = 52, n = 20, m = 20, k = 10.
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  3. #3
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    Hello, addison!

    There are 20 white marbles and 32 black marbles in a bag.
    What is the probability of drawing 20 marbles where 10 are white and 10 are black?
    There are: . {52\choose20} possible outcomes.

    To draw 10 white marbles, there are: . {20\choose10} ways.

    To draw 10 black marbles, there are: . {32\choose10} ways.

    . . Hence, there are:\ . {20\choose10}{32\choose10} ways to get 10 white and 10 black marbles.


    Therefore: . \boxed{P(\text{10 white, 10 black}) \;=\;\frac{{20\choose10}{32\choose10}}{{52\choose2  0}}}

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