Question

At a raffle, 1000 tickets are being sold for $10 each. There is one prize of $500, two prizes of $250, three prizes of $150, and four prizes of $75. If you buy one ticket, what is the expected value of your gain?

Answer 1

The expected value of the gain for buying one raffle ticket at $10, with various prizes, is calculated as -$8.35, indicating an expected loss.

Step-by-step explanation:

To calculate the expected value of your gain in a raffle, you must first consider the probability of winning each prize and what the gain from each would be. The gain is the prize amount minus the cost of the ticket.

For the $500 prize, the probability of winning is 1/1000 and the gain is $500 - $10 = $490. Two prizes of $250 give a probability of 2/1000 each, with a gain of $240 for each. With three prizes of $150, the probability is 3/1000 each, and the gain is $140 each. Finally, for the four prizes of $75, the probability is 4/1000 for each, with a gain of $65.

To find the expected value, you multiply each gain by its probability and sum them all. So, the expected value (EV) of your gain would be:

EV = (1/1000 * $490) + (2/1000 * $240) + (3/1000 * $140) + (4/1000 * $65) - (1 * $10)

EV = $0.49 + $0.48 + $0.42 + $0.26 - $10

EV = $1.65 - $10

EV = -$8.35

The expected value of your gain after buying a ticket for $10 is therefore -$8.35, which is a loss, not a gain.