Final answer:
The fair price of a lottery ticket, for which the expected value is -$2.00 and the cost is $5, is $0.35. This is the price at which the expected value is zero, meaning that on average, there is neither gain nor loss for the player or the lottery issuer.
Step-by-step explanation:
The question asks us to determine the fair price of a lottery ticket, given that its expected value is -$2.00 and its cost is $5. The expected value is a measure of the central tendency of a probability distribution and represents the average amount one can expect to win or lose per bet if the bet is made repeatedly. To find the fair price of a ticket, we look for a price at which the expected value is zero, implying that, on average, neither the player nor the lottery company makes a gain or loss.
A fair price would be determined by setting up an equation where the cost of the ticket results in an expected value of zero. Given that the expected value at a ticket price of $5 is -$2.00, this indicates that for every ticket sold, you are expected to lose $2.00 on average. However, if we want the game to be fair, players should expect to neither gain nor lose money in the long run, so we adjust the ticket price to reflect this balance. This fair price is the cost that would result in an expected value of zero.
We know that the current expected value when purchasing a ticket is -$2.00, and the ticket is priced at $5.00. To correct this imbalance and find the fair price, we would subtract the negative expected value from the ticket price: $5.00 - (-$2.00) = $5.00 + $2.00 = $7.00. But since the expected value is representative of the loss, this would mean the lottery is overpriced, and we need a price lower than $5 to make it fair. If $0.35 is the fair value as calculated by another method, this is the price where the expected value would be zero. Therefore, a fair price for the lottery ticket is $0.35.