Chapter 5, Problem 5.4.2CP

Sagittarius Casino
The Sagittarius Casino's strategy for establishing a competitive advantage over its competitors is to create unique and interesting new games for its customers to play. Sagittarius management feels it is time for the casino to once again introduce a new game to excite its customer base, and Sagittarius' s Director of Research and development, Lou Zerbit, believes he and his staff have developed a new game that will accomplish this goal. The game, which they have named POSO! (an acronym for Payouts On Selected Outcomes), is to be played in the following manner. A player will select two different values from 1, 2, 3, 4, 5, and 6. Two dice are then rolled. If the first number the player selected comes up on at least one of the two dice, the player wins $5.00; if the second number the player selected comes up on both of the dice, the player wins $10.00. If neither of these events occurs, the player wins nothing.
For example, suppose a player fills out the following card for one game of POSO!

When When the two dice are rolled, if at least one die comes up 4 the player will win $5.00, if both dice come up 2 the player will win $10.00, and if any other outcome occurs the player wins nothing.
Managerial Report
Sagittarius management now has three questions about POSO! These questions should be addressed in your report.
2. What is the expected amount a player will win when playing one game of POSO!?