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Math Help - Conditional Probability

  1. #1
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    Feb 2011
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    Conditional Probability

    Box A has 1 red and 2 white balls, whereas box B has 1 red and 1 white ball. Two balls are randomly selected, without replacement, from box A and placed in box B. If you now select a ball at random, from box B, what is the probability that is it red?

    Im stuck as I dont know what method to use to go about this question.
    Thanks
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  2. #2
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    Feb 2011
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    Well, there are two possibilities for our what our final box B looks like right before we draw from it.

    First, we could have taken 1 red and 1 white from Box A. This occurs with probability 2/3.

    Secondly, we could have taken 2 white balls from Box A. This occurs with probability 1/3.

    Under the first scenario, we will be drawing from a box that has 2 red and 2 white, and so we will have a 2/4 or 1/2 chance to get a red ball.

    Under the second scenario, we will be drawing from a box that has 1 red and 3 white balls. This gives us a 1/4 chance to get a red ball.

    (2/3)(1/2)+(1/3)(1/4) = (1/3)+(1/12) = (5/12)
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