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Probability - Gravner-57

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An urn contains $11$ balls, $3$ white , $3$ red, and $5$ blue balls. Take out $3$ balls at random, without replacement. You win $1$ for each red ball you select and lose a $1$ for each white ball you select. Determine the p.m.f. of $X$ , the amount you win.
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$P(X=3) = P(X=-3) = \frac{1}{165}$

$P(X=2) = P(X=-2) = \frac{15}{165}$

$P(X=1) = P(X=-1) = \frac{39}{165}$

$P(X=0) = \frac{55}{165}$

You can verify that sum of Probability Mass Function over all possible value of X is Equal to 1.

 

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