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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.

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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

Expected value of a ticket and Fair price of a ticket is -$2.6 and $0.4

Given that;

Number of ticket sold = 500

Cost of each ticket = $3

Prize = $200

Find:

Expected value of a ticket

Fair price of a ticket

Computation:

Expected value = [$200 - $3](1/500) - 3(499/500)  

Expected value = [$197](1/500) - 3(499/500)

Expected value = [$0.394] - [$2.994]

Expected value = -$2.6

Fair price of a ticket = ($200 - x)(1/500) = x(499/500)

Fair price of a ticket = $200 - x = 499x

Fair price of a ticket = $200 = 500x

Fair price of a ticket = $0.4

Learn more:

https://brainly.com/question/2274058?referrer=searchResults

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