pg 620 In one version of the game Keno the house has a pot c

pg 620

In one version of the game Keno, the house has a pot containing 80 balls numbered 1 through 80. A player buys a ticket for $1 and marks one number on it from 1 to 80. The house then selects 20 of the 80 members at random. If the number selected by the player is among the 20 selected by the management, the player is paid $3.20. Find the expeced net winnings for the game.

Solution

Probability that the player is chosen = 79C19 / 80C20 = 0.25

As number if ways that player is chosen = No. of ways of selecting 19 others while the player is selected

Net Winning when chosen = 3.20 - 1 = 2.20

Net winnings when not chosen = -1

Expected net winnings = 0.25*2.20 + (1-0.25)*(-1) = 0.55 - 0.75 = -0.20 $