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)?
expected value=(1/834 *(1214)) -14
This is expected value of the ticket before purchase.
one expects to lose 12.54 on each ticket.
To calculate the expected value, we need to multiply each possible outcome by its probability and then sum them up.
In this case, there are two possible outcomes: winning and not winning.
Let's calculate the expected value step by step:
1. Winning:
- The probability of winning can be determined by dividing the number of tickets you bought by the total number of tickets sold.
- Assuming you bought x tickets, the probability of winning is x/834.
- The outcome of winning is $1200 + the cost of the ticket ($14), so the value of winning is $1214.
- The probability of winning is x/834, and the value of winning is $1214, so the product of these is (x/834) * 1214.
2. Not winning:
- The probability of not winning is 1 minus the probability of winning, which can be calculated as (834 - x)/834.
- The outcome of not winning is just the negative cost of the ticket, since you only lose the money you spent.
- The probability of not winning is (834 - x)/834, and the value of not winning is -14.
- The product of the probability and the value of not winning is (834 - x)/834 * (-14).
To calculate the expected value, we sum the two possibilities:
Expected Value = (x/834) * 1214 + (834 - x)/834 * (-14)
So, for someone who buys a ticket, the expected value is given by this equation. To obtain a specific value for the expected value, you would need to plug in the number of tickets bought (x) into the equation and solve it.