I buy one of 250 raffle tickets for $10. The sponsors then randomly select 1 gra

Question

I buy one of 250 raffle tickets for $10. The sponsors then randomly select 1 grand prize worth $500, then 2 second prizes worth $200 each, and then 5 third prizes worth $50 each. The selections are made without replacement

(a) Complete the probability distribution for this raffle. Give your probabilities as a decimal (rounded to 4 decimal places) or as a fraction.

(b) Recognizing that I spent $10 to buy a ticket, determine the expected value of this raffle to me as a player. Round your answer to the nearest penny.

(c) What is an accurate interpretation of this value?

It represents how much you would win every time you play the game.

It represents the per-game average you would win/lose if you were to play this game many many times.

It represents how much you would lose every time you play the game.

It is meaningless because you can't actually win or lose this amount.

Outcomes          P(x)          Win Grand Prize     Win a Second Prize     Win a Third Prize     Win Nothing    

Explanation / Answer

Probabilities are given by: Number of prizes for that stand / Total number of tickets

a. So P(X) is computed as:

b. Expected value of raffle = (1/250) * 500 + (1/125) * 200 + (1/50) * 50 - 10

(-10 as you paid for the raffle)

= -5.4

c. Correct interpretation:

It represents the per-game average you would win/lose if you were to play this game many many times.

Outcomes          P(x)          Win Grand Prize     1/250 Win a Second Prize     2/250 = 1/125 Win a Third Prize     5/250 = 1/50 Win Nothing     1 - (1+2+5)/250 = 242/250 = 121/125

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