The Correct Answer and Explanation is:
The correct answer is a loss of $0.45.
To determine the expected profit or loss from purchasing a raffle ticket, we need to calculate the expected value. Expected value represents the average outcome you would expect if you were to participate in this raffle many times. The calculation involves considering all possible outcomes, their monetary values, and their probabilities.
First, let’s identify the prizes and their quantities. There is one $25 gift certificate, one $15 gift certificate, and three $5 gift certificates. The total number of tickets sold is 100.
Next, we calculate the probability of winning each prize. The probability is the number of a specific prize divided by the total number of tickets.
- The probability of winning the $25 prize is 1 out of 100, or 1/100.
- The probability of winning the $15 prize is 1 out of 100, or 1/100.
- The probability of winning a $5 prize is 3 out of 100, or 3/100.
Now, we can find the expected winnings. This is done by multiplying the value of each prize by its probability and then summing these results.
- Contribution from the $25 prize: $25 * (1/100) = $0.25
- Contribution from the $15 prize: $15 * (1/100) = $0.15
- Contribution from the $5 prizes: $5 * (3/100) = $0.15
The total expected winnings per ticket is the sum of these values: $0.25 + $0.15 + $0.15 = $0.55. This means that, on average, each ticket is worth $0.55 in prize money.
Finally, to find the expected profit or loss, we subtract the cost of the ticket from the expected winnings. Each ticket costs $1.
Expected Profit/Loss = Expected Winnings – Cost of Ticket
Expected Profit/Loss = $0.55 –
1.00=−1.00=−0.45
The result is a negative number, which indicates an expected loss. Therefore, the expected loss for purchasing one ticket is
0.45.Thismakessenseforaraffledesignedtoraisemoney,asthetotalvalueofprizes(0.45.Thismakessenseforaraffledesignedtoraisemoney,asthetotalvalueofprizes(55) is less than the total revenue from ticket sales ($100).
