100 raffle tickets are sold for $3 with one grand prize of $200. Julie purchased one ticket. What is her expectation? What is the fair value of a ticket?
Her expectation of winning is 1%. The fair value is $200/100 = $2.00
To determine Julie's expectation and the fair value of a ticket, we need to calculate the expected value of winning the grand prize.
The expected value (EV) is calculated by multiplying the probability of winning (P) by the value of the prize (V), and subtracting the cost of a ticket (C):
EV = P * V - C
First, let's calculate the probability of winning. There is only one grand prize, and a total of 100 tickets sold. Therefore, the probability of winning for any individual ticket is 1/100.
P = 1/100
The value of the prize is given as $200.
V = $200
The cost of a ticket is $3.
C = $3
Now, let's substitute these values into the EV formula:
EV = (1/100) * $200 - $3
= $2 - $3
= -$1
The expectation is negative (-$1), which means, on average, Julie can expect to lose $1 for every ticket she purchases. Therefore, her expectation is that she will lose money by buying a ticket.
To find the fair value of a ticket, we need to calculate the average amount that people can expect to win or lose per ticket.
So, we divide the expected value by the number of tickets sold:
Fair Value = EV / Number of Tickets
= -$1 / 100
= -$0.01
The fair value of a ticket is -$0.01, which means, on average, each ticket is worth $0.01 less than its purchase price.