Question

Find the expected and answer the qtnstions based on the given scenario.

You and a friend have created a carnival game for your classmates. You plan to charge $2 for each time a
plays, ond the payout for a win is SS. According to your calculations, the probability of a Win is .1,
What is your expected value for this game?
Mathematically, is your game considered a fair' game for you and the players?

Answer 1

The expected value of this game is -$1.3, indicating that, on average, you would expect to lose $1.3 each time you play. The game is unfair for both the players and you.

Step-by-step explanation:

In order to find the expected value of this game, we need to multiply the probability of each outcome by the amount of money won or lost for that outcome. Let's calculate:

1. The probability of winning is 0.1, and the payout for a win is $5. So the expected value for winning is 0.1 * $5 = $0.5.
2. The probability of losing is 0.9, and the loss for a loss is $2. So the expected value for losing is 0.9 * (-$2) = -$1.8.
3. Now we can find the overall expected value by summing up the expected values for winning and losing: $0.5 + (-$1.8) = -$1.3.

Since the expected value is negative, this means that, on average, you would expect to lose $1.3 each time you play the game. Therefore, the game is considered unfair for both the players and you.