SOLUTION: One thousand tickets are sold at $2 each. One ticket will be randomly selected and the winner will receive a color television valued a $387. what is the expected value for a person

Click here to see ALL problems on Probability-and-statistics

Question 1130426: One thousand tickets are sold at $2 each. One ticket will be randomly selected and the winner will receive a color television valued a $387. what is the expected value for a person that buys one ticket?
Found 2 solutions by Boreal, greenestamps:
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
E(X)=sum of x*p(x), with one x being 387 and the other -2, p(x)
(1/1000)*387-(999/1000)2
=0.387-1.998
=-$1.611 or -$1.61

Answer by greenestamps(13203) (Show Source):
You can put this solution on YOUR website!

The answer from the other tutor is off just a bit. He counted the value of the winning ticket as +$387, which is the value of the prize. But the winning ticket cost $2, so the value of the winning ticket is +$385.

Note that in this expected value problem the easiest way to find the expected value of one ticket is to look at the total cost of the tickets and the total value of the prize. 1000 tickets were sold at $2 each; to the ticket buyers, the cost of all the tickets was $2000 -- that is, the VALUE of all the tickets is -$2000. The single prize has a value of +$387; so the overall value of all the tickets is -$2000 + $387 = -$1613. Then the expected value of one ticket is -$1613/1000 = -$1.613.