An urn contains 11 balls, 3 white, 3 red, and 5 blue balls. Take out two balls at random, without replacement. You win $1 for each red ball you select and lose a $1 for each white ball you select. Let X be the random variable that notes the amount you win. Find the probability mass function (p. m.f.) of X.

Given: An urn contains 11 balls, 3 white, 3 red, and 5 blue balls.

You win $1 for each red ball you select and lose a $1 for each white ball you select.

Let X be the number of times you win.

The total number of ways to select 2 balls (order does not matter) =

The number of ways so that two balls are white (and

The number of ways so that two balls are red (and

The number of ways so that one ball is red, one is white (and

The number of ways so that two balls are blue (and ):

i.e.

The number of ways so that one ball is blue, one is white (and ):

The number of ways so that one ball is blue, one is red (and ):

Thus, the probability mass function (p.m.f.) of X would be ( in attachment) :

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