Lottery: I buy one of 200 raffle tickets for $10. The sponsors then randomly sel
ID: 3269881 • Letter: L
Question
Lottery: I buy one of 200 raffle tickets for $10. The sponsors then randomly select 1 grand prize worth $250, 2 second prizes worth $100 each, and 3third prizes worth $50 each. Below is the discrete probability distribution for this raffle.
(a) 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.
$
(b) What is an accurate interpretation of this value?
It is meaningless because you can't actually win or lose this amount.It represents how much you would lose every time you play the game. 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.
(c) Based on your answers, would this raffle be a good financial investment for you and why? There is only one correct answer and reason.
Yes, because the expected value is positive.Yes, because the expected value is negative. No, because the expected value is positive.No, because the expected value is negative.
Prize P(x) Grand 1/200 Second 2/200 Third 3/200 None 194/200Explanation / Answer
Expected value of the raffle to us
= - Cost of ticket + Expected winning amount
= -10 + (1/200)*(250) + (2/200)*(100) + (3/200)*(50)
= -10 + 1.25 + 1 + 0.75
= -7
Therefore the expected value of the raffle to a plyer would be -7 dollars
b) The expected value is defined as the per-game average you would win/lose if you were to play this game many many times. Therefore if we play the raffle for n number of times and n tends to infinity then we are expected to lose 7n dollars in total
Therefore It represents the per-game average you would win/lose if you were to play this game many many times.
c) This raffle ticket would not be a good financial investment because the expected value of playing it is negative
Therefore No, because the expected value is negative.
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