Tickets for a raffle cosr
$
$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)?
If the Expected Value is negative, be sure to include the "-" sign with the answer. Express the answer rounded to two decimal places.
12.53
To find the expected value, you need to calculate the product of each possible outcome with its corresponding probability and then sum up these values.
In this case, there are two possible outcomes:
1. Winning the raffle: The probability of winning is 1 out of 834 since there is only one winner among the 834 tickets sold. The value of winning is $1200 + $14 (the cost of the ticket) = $1214.
2. Not winning the raffle: The probability of not winning is 833 out of 834 since only one ticket is selected as the winner out of the 834 tickets sold. The value of not winning is -$14 (the cost of the ticket).
To calculate the expected value, you can use the following formula:
Expected Value = (Probability of winning * Value of winning) + (Probability of not winning * Value of not winning)
Expected Value = (1/834 * $1214) + (833/834 * -$14)
Calculating this expression will give you the answer:
Expected Value = ($1.45516983) + (-$13.99396896) ≈ -$12.54
Therefore, the expected value, rounded to two decimal places, is -$12.54, which means on average, a person who buys a ticket can expect to lose $12.54.