The PTA is holding a raffle. The prize is a camera worth $200. Each raffle ticket costs $5. One hundred tickets are sold and a winner is drawn at random.

Find the expected value of the purchase of a ticket. (Use a negative sign in your answer, if necessary.)

Question

The PTA is holding a raffle. The prize is a camera worth $200. Each raffle ticket costs $5. One hundred tickets are sold and a winner is drawn at random.

Find the expected value of the purchase of a ticket. (Use a negative sign in your answer, if necessary.)

Vocaloid · Answer

On my phone, apologies for formatting

Expected value = (value of an event)(probability of an event) summed across all values

In the context of the problem, you have a 1/100 probability of winning 200 (technically 195 after you subtract the cost of the ticket) and a 99/100 of losing 5 (so the value is -5)

Using the formula, we have (1/100)(195) + (99/100)(-5)