Four thousand raffle tickets are sold for $1 each. Three prizes will be awarded,

Question

Four thousand raffle tickets are sold for $1 each. Three prizes will be awarded, one for $1,500 and two for $750. Assume that the probability that any given ticket is selected for the $1,500 prize is and the probability that any given ticket is selected for a $750 prize is refunded to them. Jennifer purchases one of these tickets. Complete parts (a) and (b) below. (a) Determine Jennifer's expected value 2 Winners do not have their ticket costs of $1 4,000 4,000 $(Type an integer or a decimal rounded to the nearest hundredth as needed.) (b) Determine the fair price of a ticket. $(Type an integer or a decimal rounded to the nearest hundredth as needed.)

Explanation / Answer

SOLUTION:

(a) Jennifer can win a net of 1500 – 1 = 1499 with a probability of 1/4000, 750 – 1 = 749 with a probability of 2/4000 and 0 – 1 = -1 with a probability of 3997/4000

Expected value = 1499(1/4000) + 749(2/4000) + (-1)(3997/4000) = -1/4

Expected value = $-0.25

(b) Let the fair price of a ticket be p. Then (1500 – p)(1/4000) + (750 – p)(2/4000) + (-p)(3997/4000) = 0

Solving, we get p = 3/4

Fair price of a ticket = $0.75

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