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Math Help - Probability distribution when with replacement

  1. #1
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    Probability distribution when with replacement

    Five balls are drawn from an urn containing 4 white and 6 black balls. Find the probability distribution of the number of white balls drawn when the balls are drawn with replacement.

    Please help me in solving the above problem.
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  2. #2
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    It would be quite simple to give you the name of the distribution and just go and read it. But let me try to make you find the solution.

    In how many ways can you draw 5 balls from an urn with replacement?
    In how many ways can you draw k white balls AND 5-k black balls (with replacement)?
    let's suppose that k=2, then a possible draw would be WBBBW. But does it matter to you if it is WBBBW or BBBWW or BWBWB?

    You can also try to reason in this way: what is the probability of drawing ONE white ball? Does this probability change on the next draw? (remember that it is with replacement). Again consider the WBBBW or BWBWB etc situation.
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