I buy one of 250 raffle tickets for $20. The sponsors then randomly select 1 gra
ID: 3290420 • Letter: I
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 NothingExplanation / 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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