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Discrete Distributions: Chips Being Red

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Let X equal the number of "ones" if a fair dice is tossed two independent times by someone out in the hall. If X=x that person gives the player a bowl consisting of 10-3x red chips and 3x white chips. The player then selects one chip at random from the bowl. What is the conditional probability that X=0 given that the chip is red? How does this compare to the prior probability P(X=0)?

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In the solution the discrete distributions of chips being red are discussed. The conditional probability is determined. See attachment.

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By Bayes theorem,

The probability of getting one in a toss of a fair dice is 1/6, and X is the binomial random variable with N=2, and p=1/6. Then we have the probability distribution ...

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