Question

You purchase a raffle ticket to help out a charity. The raffle ticket costs $5. The charity is selling 2000 tickets. One of them will be drawn and the person holding the ticket will be given a prize worth $4000. Compute the expected value for this raffle.

Answer 1

The expected value of buying a $5 raffle ticket with a 1/2000 chance of winning a $4000 prize is approximately -$2.995, indicating an expected loss.

Step-by-step explanation:

The student is asking about the expected value of participating in a raffle. To calculate this, we take into account the probability of winning the prize and the cost of the ticket. With 2000 tickets sold and a prize worth $4000, the probability of winning is 1/2000. If the ticket costs $5, the expected value (EV) of a ticket can be calculated using the formula EV = (probability of winning × prize value) - (probability of losing × cost of ticket).

The probability of losing the raffle is 1999/2000 (since there's only one winner), so EV = (1/2000 × $4000) - (1999/2000 × $5).
This simplifies to EV = ($2) - ($4.995) = -$2.995. Therefore, the expected value of buying a raffle ticket in this scenario is approximately -$2.995.

Answer 2

-$3

Step-by-step explanation:

Data provided in the question:

Cost of raffle ticket = $5

Number of tickets sold = 2000

Probability of winning = 1 ÷ 2000 = 0.0005

Winning prize = $4,000

Now,

The expected value of prize = Probability of winning × Winning prize

= 0.0005 × $4,000

= $2

Therefore,

The expected value for this raffle

= expected value prize - Cost of raffle ticket

= $2 - $5

= -$3