Question

Use the following statement to answer parts ​a) and​ b). Five hundred raffle tickets are sold for​ $3 each. One prize of ​$200 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

Answer:

A.) - 2.6

B.) 0.4

Explanation:

Ticket price = $3

Winning price = $200

Probability of winning(Pwin) = (1/500)

Probability of not winning (Ploss) = [ 1 - (1/500)] = 499/500

Net income if Raul wins (Nwin) = $200 - $3 = $197(no refund)

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

A.) Expected value is calculated by;

(Pwin × Nwin) + (Ploss × Nloss)

((1/500) × 197) + ((499/500) × - 3)

0.394 - 2.994 = - 2.6

B.) Fair Value is calculated by;

Cost of ticket + Expected value

3 - 2.6 = 0.4