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22 October, 06:59

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.)

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Answers (2)
  1. 22 October, 07:07
    0
    A.) - 2.8

    B.) 0.2

    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
  2. 22 October, 07:16
    0
    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

    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
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