Problem

In Example 1d, compute the conditional probability that we win i dollars, given that we...

In Example 1d, compute the conditional probability that we win i dollars, given that we win some-thing; compute it for i = 1, 2, 3.

Reference:

Three balls are randomly chosen from an urn containing 3white, 3 red, and 5 black balls. Suppose that we win $1 for each white ball selected and lose $1 for each red ball selected. If we let X denote our total winnings from the experiment, then X is a random variable taking on the possible values 0,±1, ±2, ±3 with respective probabilities.

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