I buy one of 250 raffle tickets for $20. The sponsors then randomly select 1 gra

Question

I buy one of 250 raffle tickets for $20. The sponsors then randomly select 1 grand prize worth $600, then 2 second prizes worth $200 each, and then 3 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 $20 to buy a ticket, determine the expected value of this raffle to me as a player. Round your answer to the nearest penny.
dollars

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

It represents how much you would lose 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 is meaningless because you can't actually win or lose this amount.It represents how much you would win every time you play the game.

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

Explanation / Answer

Answer:

I buy one of 250 raffle tickets for $20. The sponsors then randomly select 1 grand prize worth $600, then 2 second prizes worth $200 each, and then 3 third prizes worth $50 each. The selections are made without replacement.

Outcomes

x

p

         P(x)         

x*p(x)

Win Grand Prize    

600

1/250

0.0040

2.4000

Win a Second Prize    

200

2/249

0.0080

1.6064

Win a Third Prize    

50

3/247

0.0121

0.6073

Win Nothing    

-20

1-(1/250+2/249+3/247)

0.9758

-19.5164

Total

-14.9027

(b) Recognizing that I spent $20 to buy a ticket, determine the expected value of this raffle to me as a player. Round your answer to the nearest penny.
-14.90 dollars

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

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

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

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

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

Outcomes

x

p

         P(x)         

x*p(x)

Win Grand Prize    

600

1/250

0.0040

2.4000

Win a Second Prize    

200

2/249

0.0080

1.6064

Win a Third Prize    

50

3/247

0.0121

0.6073

Win Nothing    

-20

1-(1/250+2/249+3/247)

0.9758

-19.5164

Total

-14.9027

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