SOLUTION: One thousand tickets are sold at $1 each. One ticket will be randomly selected and the winner will receive a color television valued at $398. What is the expected value for a pers

Question 1028126: One thousand tickets are sold at $1 each. One ticket will be randomly selected and the winner will receive a
color television valued at $398. What is the expected value for a person that buys one ticket?
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Question:
One thousand tickets are sold at $1 each. One ticket will be randomly selected and the winner will receive a
color television valued at $398. What is the expected value for a person that buys one ticket?

Solution:
Expected value E[x]=μ is the overall average value of the game, defined by
E[x]=∑ x*P(x) where the summation is taken over all outcomes.
x=value of an outcome,
P(x)=probability of that outcome.

For the given problem, we have 1000 tickets, out of which one will win a television worth 398. That means 999 people will pay $1 (with a probability of 999/1000 losing) , and the winner will get a value of $398-$1=$397 with a probability of 1/1000 winning).
Summing over the whole population,
E[x]=(-1)*999/1000+(397)*1/1000=-602/1000=-0.602 (in dollars)
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