Michael is playing a game of chance in which he rolls a number cube. This game is this: Michael rolls the number cube once. He wins S1 if a 1 is rolled, S2 if a 2 is rolled, and S3 if a 3 is rolled. He loses $2.50 if a 4, 5, or 6 is rolled. (a) Find the expected value of playing the game. (b) What can Michael expect in the long run, after playing the game many times?
Question:
Michael is playing a game of chance in which he rolls a number cube. This game is this: Michael rolls the number cube once. He wins S1 if a 1 is rolled, S2 if a 2 is rolled, and S3 if a 3 is rolled. He loses $2.50 if a 4, 5, or 6 is rolled. (a) Find the expected value of playing the game. (b) What can Michael expect in the long run, after playing the game many times?
Choices:
- Michael can expect to gain money. He can expect to win dollars per roll.
- Michael can expect to lose money. He can expect to lose dollars per roll.
- Michael can expect to break even (neither gain nor lose money).
Answer:
Michael can expect to lose money. He can expect to lose dollars per roll.