Question

Eight hundred chances are sold at $3 apiece for a raffle. There is a grand prize of $550, two second prizes of $350, and five third prizes of $150. First, calculate the expected value of the lottery. Determine whether the lottery is a fair game. If the game is not fair, determine a price for playing the game that would make it fair.

Answer 1

To calculate the expected value of the lottery, multiply each prize by its probability of being won and sum them up. The expected value of the lottery is $2.5. The game is not fair and the price for playing the game should be set to $2.5.

Step-by-step explanation:

To calculate the expected value of the lottery, we need to multiply each prize by its probability of being won and then sum them up. Let's calculate:

1. The grand prize of $550 has a probability of winning of 1/800, so its contribution to the expected value is (1/800) * $550 = $0.6875.
2. The two second prizes of $350 each have a probability of winning of 2/800, so their contribution is (2/800) * $350 = $0.875.
3. The five third prizes of $150 each have a probability of winning of 5/800, so their contribution is (5/800) * $150 = $0.9375.

The sum of these contributions is $0.6875 + $0.875 + $0.9375 = $2.5.

The expected value of the lottery is $2.5. Since the cost of buying a raffle ticket is $3, the game is not fair. To make it a fair game, the price for playing the game should be set to $2.5, which is the expected value.