Question 40937: Suppose you buy one ticket for a dollar out of a lottery of a 1000 tickets. Where the prize is $500. What is your expected value? Found 2 solutions by mbarugel, stanbon:Answer by mbarugel(146) (Show Source):
You can put this solution on YOUR website! Hello!
The formula for the expected value would be:
Expected Value = (Probability of Winning)*(Prize if won) + (Probability of not winning)*(Prize if not won)
The price you get if you don't win is 0, so we can ignore the 2nd term. Now, the probability of winning is 1/1000, because you bought 1 ticket out of 1000. Since the prize is $500:
Exp. Value = (1/1000)*500 = $0.50
You can put this solution on YOUR website! Suppose you buy one ticket for a dollar out of a lottery of a 1000 tickets. Where the prize is $500. What is your expected value?
Your probability of winning is 1/1000
So your expected gain is (1/1000)(500)]= 0.50 dollar
You expected losing is 999/1000 (-1)= .99 dollar
Adding these you get an expected value of -.49 dollar
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Comment: Sometimes (but not always) these problems take
into account that you are spending $1 for the ticket so
the 500 prize is really a gain of $499. If your text
takes that approach your expected gain is not 0.50 but
rather it is 0.499. Adding that to -.99 you would get
an answer of 0.491.
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In either case if you round out to the nearest penny
the expected value is -0.49 dollar
Cheers,
Stan H.
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