Question

Use the following statement to answer parts ​a) and​ b). Five hundred raffle tickets are sold for​ $3 each. One prize of ​$100 is to be awarded. Winners do not have their ticket costs of​ $3 refunded to them. Raul purchases one ticket. ​a) Determine his expected value. ​b) Determine the fair price of a ticket. ​a) His expected value is ​$ nothing. ​(Type an integer or a​ decimal.)

Answer 1

A) he would make a loss of $2.79 of his ticket purchase hence the expected value of the ticket will be $3 - $2.79 = $0.21

B) fair price of a ticket = $0.20

Step-by-step explanation:

A) The expected value

The variables are : winner prize = +$100 and -$3 ( not refunded )

The probability of winning the prize = 1/500 and 499/500 for not winning

therefore the expected value E(x) would be

= 100 * 1/500 + ( -3 ) * 499/500

= $0.2 - $2.99

= -$2.79 he would make a loss of $2.79 of his ticket purchase hence the expected value of the ticket will be $3 - $2.79 = $0.21

B) the fair price of the ticket would be

lets assume the fair price to be "y"

The random variables are $100 and -y

the corresponding probabilities of winning and not wining are : 1/500 and 499/500

= (100 * 1/500) + (-y * 499/500) = 0

= 100/500 - 499 y/500 = 0

= 100 - 499 y = 0

therefore y = 100 /499 = $0.20 fair value of the ticket

Answer 2

Answer:

A.) - 2.8

B.) 0.2

Step-by-step explanation:

Ticket price = $3

Winning price = $100

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

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

Net income if Raul wins (Nwin) = $100 - $3 = $97

Net loss if Raul loss (Nloss) = - $3

A.) Calculation of Expected value

(Pwin × Nwin) + (Ploss × Nloss)

((1/500) × 197) + ((499/500) × - 3)

0.194 - 2.994 = - 2.8

B.) Calculation of Fair Value ;

Cost of ticket + Expected value

3 - 2.8 = 0.2