Final answer:
The expected gain or loss for buying a lottery ticket in a raffle with one ticket is an expected loss of $1.30. This is calculated based on the price of the ticket and the probability of winning the available prizes.
Step-by-step explanation:
The question asks us to calculate the expected gain or loss for buying a lottery ticket in a raffle. To find this, we need to consider the cost of the ticket and the potential prizes receivable. Let's assume, in this scenario, that each ticket costs $10. There are various prizes available: one $500 prize, two $100 prizes, and four $25 prizes with a total of 100 tickets.
To calculate the expected value, we multiply the value of each prize by the probability of winning that prize. The probability of winning the $500 prize is 1/100, the probability of winning a $100 prize is 2/100 (as there are two such prizes), and the probability of winning a $25 prize is 4/100 (since there are four such prizes). Any ticket that does not win a prize results in a $10 loss, which is the cost of the ticket.
Expected Value Calculation:
- $500 prize: 1/100 chance of winning $500 = $5
- $100 prize: 2/100 chance of winning $100 = $2
- $25 prize: 4/100 chance of winning $25 = $1
- No prize: 93/100 chance of losing $10 = -$9.30
Adding these together, the expected value of buying one ticket is $5 + $2 + $1 - $9.30 = -$1.30. Therefore, on average, one would expect to lose $1.30 per ticket purchased in this raffle.