Five hundred raffle tickets were sold for $2 each. A prize of $400 is to be awarded. If you buy one ticket, determine the expected value. What is the fair price for a ticket?

To determine the expected value, we need to calculate the probability of winning and the amount of money won.

First, let's calculate the probability of winning. Since there are 500 tickets sold and 1 prize, the probability of winning with a single ticket is 1/500.

Now, let's calculate the amount of money won. There is a total prize of $400, so if you win, you will receive $400.

To calculate the expected value, we multiply the probability of winning by the amount won:
Expected Value = Probability of Winning * Amount Won

In this case, the expected value is:
Expected Value = (1/500) * $400 = $0.80

Therefore, the expected value of buying one ticket is $0.80.

To determine the fair price for a ticket, we look at the expected value. The fair price is the price at which the expected value is equal to the cost of the ticket. In this case, since the expected value is $0.80, the fair price for a ticket would be $0.80 or lower. If the ticket price is higher than $0.80, it would not be considered fair.