There is a $2 raffle with a first prize of $10000, a second prize of $500, and a 3rd prize of $100. If 1000 tickets are sold find the expected value. How much should the raffle ticket cost to make this a fair game?
A fair game would be when the price of all the tickets sold is equal to the total prize money. That is $10600.
So the price of one ticket would need to be just one-thousandth of that.
i just need help
To find the expected value of a raffle ticket, we need to calculate the average amount of money you could expect to win if you were to buy a large number of tickets.
First, let's calculate the probability of winning each prize:
- The probability of winning the first prize is 1 in 1000 (since there is only one first prize and 1000 tickets).
- The probability of winning the second prize is also 1 in 1000.
- The probability of winning the third prize is 1 in 1000.
Next, let's calculate the amount of money you could expect to win for each prize:
- The expected value of the first prize is $10,000.
- The expected value of the second prize is $500.
- The expected value of the third prize is $100.
Now, let's calculate the expected value of the raffle ticket. We multiply the probability of winning each prize by the corresponding expected value and sum them up:
Expected value = (probability of winning first prize * expected value of first prize) + (probability of winning second prize * expected value of second prize) + (probability of winning third prize * expected value of third prize)
Expected value = (1/1000 * $10,000) + (1/1000 * $500) + (1/1000 * $100)
Expected value = $10 + $0.5 + $0.1
Expected value = $10.60
Therefore, the expected value of the raffle ticket is $10.60.
To make this a fair game, the ticket price should also be $10.60.