Question

Five thousand tickets are sold at $1 each for a charity raffle. Tickets are to be drawn at random and monetary prizes awarded as follows: 1 prize of $900, 3 prizes of $300, 5 prizes of $30, and 20 prizes of $5. What is the expected value of this raffle if you buy 1 ticket? Let X be the random variable for the amount won on a single raffle ticket. E(X)dollars = (Round to the nearest cent as needed.)

Answer 1

The expected value of the raffle if you buy 1 ticket is $0.43.

Step-by-step explanation:

The expected value of the raffle can be calculated by multiplying the amount won for each prize by the probability of winning that prize, and then summing up these values. Let's calculate the expected value for the raffle:

1 prize of $900: Probability of winning = 1/5000, Expected value = $900 * (1/5000) = $0.18

3 prizes of $300: Probability of winning = 3/5000, Expected value = $300 * (3/5000) = $0.18

5 prizes of $30: Probability of winning = 5/5000, Expected value = $30 * (5/5000) = $0.03

20 prizes of $5: Probability of winning = 20/5000, Expected value = $5 * (20/5000) = $0.04

Summing up the expected values for each prize, we get: $0.18 + $0.18 + $0.03 + $0.04 = $0.43

Therefore, the expected value of the raffle if you buy 1 ticket is $0.43.