One thousand raffle tickets are sold for 1 dollar each, one prize of 800.00 dollars is to be awarded. Rene Condos purchases one ticket
a) Determine her expected value?
b) Determine the fair price of a ticket?
prob(win) = 1/1000
Expected value = (1/1000)($800) = $.80
which would a "fair" price for the ticket.
To determine Rene Condos' expected value and the fair price of a ticket, we need to calculate the probabilities of winning and losing, as well as the corresponding payoffs.
a) Determining the expected value:
The expected value is calculated by multiplying each possible outcome by its probability and summing them up.
In this case, there is only one prize of $800 awarded among the 1000 tickets sold. So the probability of winning the prize would be 1/1000, and the payoff would be $800.
Therefore, Rene Condos' expected value can be calculated as follows:
Expected Value = (Probability of Winning * Payoff) + (Probability of Losing * Payoff)
Expected Value = (1/1000 * $800) + (999/1000 * $0)
Expected Value = $0.8
So, Rene Condos' expected value is $0.8.
b) Determining the fair price of a ticket:
The fair price of a ticket is the maximum price someone should be willing to pay for a ticket, considering the expected value.
Since the expected value is $0.8, the fair price of a ticket should be equal to or less than this value to represent a fair game.
Therefore, the fair price of a ticket is $0.8 or less.
Note: In practice, various factors like entertainment value and personal preferences may influence someone's willingness to pay more for a ticket, even if the expected value is lower.