Final answer:
To calculate the expected value, multiply each possible outcome by its probability and sum them up. Assuming all 100 tickets are sold, the expected gain or loss for buying a raffle ticket that costs $10 is $10.
Step-by-step explanation:
To calculate the expected value, we multiply each possible outcome by its probability and then sum them up. In this case, we have four possible outcomes: no prize ($0), one $500 prize ($500), two $100 prizes ($200), and four $25 prizes ($100). The probabilities of these outcomes depend on the number of tickets sold. Let's assume all 100 tickets are sold. The probability of winning no prize is 96/100, the probability of winning the $500 prize is 1/100, the probability of winning a $100 prize is 2/100, and the probability of winning a $25 prize is 4/100.
Expected value = (0)(96/100) + (500)(1/100) + (200)(2/100) + (100)(4/100) = 0 + 5 + 4 + 1 = $10
Therefore, your expected gain or loss is $10. This means that, on average, you can expect to gain $10 for each raffle ticket you buy.