A gambling game involves a box containing 6 white poker chips, 11 blue poker chi

Question

A gambling game involves a box containing 6 white poker chips, 11 blue poker chips, and 83 red poker chips. The player selects one of these chips at random. If they get a white chip they receive 20 dollars if they get a blue chip they receive 6 dollars, and if they get a red chip they receive nothing. It costs 2 dollars to play the game.

Let random variable X represent the player's net gain, in dollars. Complete the probability distribution function for X in the table below. Enter the values of X in ascending order. Use negative values of X to represent a net loss, and enter only the numerical value (without using a dollar sign). Your entries should all be integers or decimals.

X Pr(X)

Explanation / Answer

Clearly we would have 3 outcomes here - one each for different colours. The probabiltiy distribution for X thus is obtained as:

Note that the probabilities are computed by dividing with the total number of chips which is 100 here.

X P(X = x) - 2 83 / 100 = 0.83 6 - 2 = 4 11 / 100 = 0.11 20 - 2 = 18 6 / 100 = 0.06

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