Question

Tickets for a raffle cost $14. There were 834 tickets sold. One ticket will be randomly selected as the winner, and that person wins $1200 and also the person is given back the cost of the ticket. For someone who buys a ticket, what is the Expected Value (the mean of the distribution)?

Answer 1

To calculate the expected value (mean) of this raffle, you need to consider the probability of winning and the potential outcomes (both the prize and the cost of the ticket). Here's how you can calculate it:

1. Probability of Winning:
- There is 1 winning ticket out of 834 tickets sold. So, the probability of winning is 1/834.

2. Prize and Cost:
- If you win, you receive $1200 as a prize, and you also get back the cost of the ticket, which is $14.

Now, calculate the expected value:

Expected Value = (Probability of Winning * Prize) - Cost of Ticket

Expected Value = (1/834 * $1200) - $14

Expected Value = ($1200/834) - $14

Expected Value ≈ $1.44 - $14

Expected Value ≈ -$12.56

So, the expected value for someone who buys a ticket is approximately -$12.56. This means, on average, a person can expect to lose about $12.56 for each ticket purchased in this raffle.