A gambling game involves a box containing 7 white poker chips, 10 blue poker chi

Question

A gambling game involves a box containing 7 white poker chips, 10 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 4 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 -- that is, the number of dollars they receive (if any) minus the number of dollars they pay to play the game.

Explanation / Answer

The PMF for X here is obtained as:

Probabilities are computed as the number of specific coloured chips / Total number of chips.

P( X = -2) = 83/100 = 0.83
P( X = -2 + 4 = 2) = 10/100 = 0.1
P( X = -2 + 20 = 18) = 7/100 = 0.07

Therefore Expected gain/loss is computed here as:

= -2*0.83 + 2*0.1 + 18*0.07

= -0.2

Therefore expected value here is - $ 0.2

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