Raffle question

Question

Tickets for a raffle cost $11. There were 826 tickets sold. One ticket will be randomly selected as the winner, and that person wins $1000 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)?

If the Expected Value is negative, be sure to include the "-" sign with the answer. Express the answer rounded to two decimal places.

Answer 1

To calculate the expected value for someone who buys a ticket in the raffle, we need to consider the probability of winning and the amount of money won.

The probability of winning is 1/826, since there is only one winning ticket out of 826 tickets sold.

The amount of money won is $1000 plus the cost of the ticket, which is $11.

Therefore, the expected value can be calculated as:

Expected Value = (Probability of winning) x (Amount won) + (Probability of not winning) x (Amount lost)

The probability of not winning is 825/826, since there is only one winning ticket out of 826 tickets sold.

The amount lost is simply the cost of the ticket, which is $11.

Putting it all together, we get:

Expected Value = (1/826) x ($1000 + $11) + (825/826) x (-$11) Expected Value = $1.19 - $10.66 Expected Value = -$9.47

Therefore, the expected value for someone who buys a ticket in the raffle is -$9.47, which means that on average, a person who buys a ticket can expect to lose $9.47 per ticket.