Final answer:
The probability that Taylor will win the raffle with one ticket out of 16 is 6.25%. To find your expected gain or loss in a raffle, consider the cost of the ticket, number of tickets, and the value of prizes. Calculate the fair price for a raffle ticket by dividing the total value of prizes by the number of tickets sold.
Step-by-step explanation:
The question pertains to the calculation of probability and expected value in a raffle scenario. To calculate the probability that Taylor will win the raffle with one ticket out of 16, we simply divide the number of winning tickets (1, since Taylor bought one ticket) by the total number of tickets (16). This yields a probability of 1/16, which can be converted to a percentage as (1/16) * 100%, resulting in 6.25%.
In order to find your expected gain or loss from buying a ticket in a raffle, you need to consider the cost of the ticket, the number of tickets, and the value of the prizes. Assume each ticket costs $10, there are 100 tickets, and the raffle prizes are one $500 prize, two $100 prizes, and four $25 prizes.
The expected value E(X) can be calculated using the formula:
- Calculate the probability of winning each prize.
- Multiply each probability by the corresponding prize value.
- Sum these amounts to find the total expected winnings.
- Subtract the cost of the ticket from the total expected winnings to find the expected gain or loss.
To break even in a raffle with multiple prizes and ticket sales, the total revenue from ticket sales should be equal to the total value of prizes distributed. The fair price to achieve this can be found by dividing the total value of the prizes by the number of tickets sold.
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