Question

You are given 2 to 1 odds against rolling two even numbers with the roll of two fair dice, meaning you win $2 if you succeed and lose $1 if you fail. Find the expected value (to you). Would you expect to lose or win money in 1 game? In 100 games?

A) Expected value: $0.50; Expect to win money in 1 game and 100 games.
B) Expected value: $1.00; Expect to win money in 1 game and 100 games.
C) Expected value: -$0.50; Expect to lose money in 1 game and 100 games.
D) Expected value: -$1.00; Expect to lose money in 1 game and 100 games.

Answer 1

The expected value is -$0.50, indicating an average loss. In 1 game and 100 games, you would expect to lose money.

Step-by-step explanation:

The expected value is found by multiplying the payoff of each outcome by its probability and summing these values. In this case, you win $2 if you roll two even numbers and lose $1 if you don't. The probability of rolling two even numbers is 9/36 because there are 9 even numbers out of 36 possible outcomes with two fair dice. The probability of not rolling two even numbers is 27/36. So, the expected value is (2 * 9/36) + (-1 * 27/36) = -1/2 or -$0.50.

If you play 1 game, you would expect to lose $0.50 on average. If you play 100 games, you would expect to lose $0.50 per game on average, resulting in a total expected loss of $0.50 * 100 = -$50. Therefore, the correct answer is C) Expected value: -$0.50; Expect to lose money in 1 game and 100 games.