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15. You enter a raffle to win a cruise from Miani to St. Croix valued at 3,000 dollars. It costs 5 dollars to buy one ticket. You are eager to take the cruise and buy twenty tickets. Suppose 2,000 tickets are sold. (a) What is the probability that you will win the cruise? Answer: 0.01 (b) If X-amount of money made or lost by entering the raffle, what is the expected value of X? Explain the meaning of this result in terms of the 100 dollar ticket purchase. Answer: -$70 (4.2.4)

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Answer #1

(a)

Number of favorable events = 20

Total number of events = 2000

So,

Probability of winning = 20/2000 = 0.01

So,

Answer is:

0.01

(b)

Event (buy 20 tickets) amount of money made or lost (variable X) Probability (P) of X PX
Win the cruise 3000-(20 X 5) = 2900 0.01 2900 X 0.01 = 29
Did not win the cruise - (20 X 5) = - 100 1 - 0.01 = 0.99 - 100 X 0.99 = - 99
Total 29 - 99 = - 70

Expected value of X = - $70

EXPLANATION:

For te 5 X $20 =$100 dollar ticket purchase, the result will be expected to be loss of $70.

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