Question

Use the following statement to answer parts a) and b). Two hundred raffle tickets are sold for $3 each. One prize of $1000 is to be awarded. Winners do not have their ticket costs of $3 refunded to them. Raul purchases one ticket.a) Determine his expected value.b) Determine the fair price of a ticket.

Answer 1

Fom the question, the following can be derived:

Ticket price = $3

Winning price = $1000

Probability of winning (Pwin) = (1/200)

Probability of not winning (Ploss) = [1 - (1/200)] = 199/200

The net income if Raul wins (Nwin) = $1000 - $3 = $997 (when there is no refund)

The net loss if Raul does not win (Nloss) = -$3

(a) We are to determine his expected value:

To determine his expected value, we using this:

(Pwin * Nwin) + (Ploss * Nloss)

((1/200) * 997) + ((199/200) * -3)

4.985 - 2.985 = 2

The expected value is 2.

(b) We are also to determine the fair price of a ticket

To get the fair price of a ticket, we will add the cost of ticket and the expected value:

Cost of ticket + Expected value

3 + 2 = 5

Therefore, the fair price of a ticket is 5.