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Math Help - [SOLVED] prob distribution

  1. #1
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    [SOLVED] prob distribution

    A drawer contains 8 brown socks and 4 blue socks. A sock is taken from the drawer at random, its color is noted and it is then replace. This procedure is performed twice more. If X is the r.v "the # of brown socks taken", find the prob distribution for X

    Can somebody explain this question to me pls!tnX
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  2. #2
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    I assume r.v. means random variable

    So we have P(brown) = \frac{8}{12} = \frac{2}{3}

    And P(blue) = \frac{4}{12} = \frac{1}{3}

    The probability distribution will be as follows:

    P(X=0) = P(blue) \times P(blue) = [P(blue)]^2 = \left(\frac{1}{3}\right)^2

    P(X=1) = P(blue) \times P(brown) + P(brown) \times P(blue) = 2 \times P(blue) \times P(brown)  = 2 \times \frac{1}{3} \times \frac{2}{3}

    <br />
P(X=2) = P(brown) \times P(brown) = [P(brown)]^2 = \left(\frac{2}{3}\right)^2

    And that's the probability distribution for X.
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