A cash prize of $5000 is to be awarded at a fundraiser. If 2,500 tickets are sold at $5 each, find the expected value if a person purchases just one ticket.
It is Correct. Sorry I said it seemed wrong.
If you buy one ticket you have a 1/2500 chance of winning. Thus, you're expected value is 5000/25$ = 2$ return for your 5$ ticket. So you get -$3.
Well, let's crunch some numbers and do some calculations! If there are 2,500 tickets sold at $5 each, we can find the total amount collected by multiplying the number of tickets by the price of each ticket. In this case, it would be 2,500 tickets multiplied by $5, which gives us a total of $12,500.
So, the expected value can be calculated by dividing the total amount collected ($12,500) by the number of tickets (2,500). Drumroll, please...the expected value of purchasing just one ticket would be $5!
But hey, keep in mind that the expected value represents the average amount you would get if you played this game many, many times. In reality, you might win the grand prize of $5,000 or walk away empty-handed. So, buckle up and enjoy the excitement of the fundraiser!
To find the expected value, we need to calculate the average amount a person can expect to win if they purchase just one ticket.
First, let's determine the total amount collected from ticket sales. Since 2,500 tickets were sold at $5 each, we can calculate the total amount as follows:
Total amount collected = Number of tickets sold × Price per ticket
Total amount collected = 2,500 × $5 = $12,500
We know that there is a cash prize of $5000 to be awarded. The remainder of the total amount collected will be distributed evenly among the ticket purchasers.
Amount distributed to ticket purchasers = Total amount collected - Cash prize
Amount distributed to ticket purchasers = $12,500 - $5000 = $7500
Next, we divide the amount distributed to ticket purchasers by the number of tickets sold to find the average amount per ticket:
Average amount per ticket = Amount distributed to ticket purchasers / Number of tickets sold
Average amount per ticket = $7500 / 2500 = $3
Therefore, if a person purchases just one ticket, their expected value would be $3.