Question

Is it worth it? Andy is always looking for ways to make money fast. Lately, he has been trying to make money by gambling. Here is the game he is considering playing: The game costs $2 to play. What is the decision Andy should make regarding playing this game?

Answer 1

To determine whether it is worth it to play the game, we need to calculate the expected value. After analyzing each possible outcome, it is clear that Andy should not play this game if his goal is to make money.

Step-by-step explanation:

To determine whether Andy should play the game, we need to calculate the expected value, which is the average net gain or loss per game. Let's analyze each possible outcome:

1. If Andy selects a face card and the coin lands on heads, he wins $6. The probability of this happening is 12/52 * 1/2 = 1/17. So, the expected gain is 1/17 * 6 = $0.35.
2. If Andy selects a face card and the coin lands on tails, he wins $2. The probability of this happening is 12/52 * 1/2 = 1/17. So, the expected gain is 1/17 * 2 = $0.12.
3. If Andy selects a non-face card, he loses $2. The probability of this happening is 40/52. So, the expected loss is 40/52 * (-2) = -$1.54.

To find the overall expected value, we sum up the expected gains and losses: $0.35 + $0.12 - $1.54 = -$1.07.

The negative expected value indicates that over the long run, Andy is expected to lose an average of $1.07 per game. Therefore, Andy should not play this game if his goal is to make money.