SOLUTION: The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $7 each and will sell 500 tickets. There is one $1,000 grand prize, two $200

Question 1150251: The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $7 each and will sell 500 tickets. There is one $1,000 grand prize, two $200 second prizes, and fourteen $10 third prizes. You just bought a ticket. Find the expected value for your profit. Round to the nearest cent.
Found 4 solutions by VFBundy, Boreal, ikleyn, greenestamps:
Answer by VFBundy(438)   (Show Source): You can put this solution on YOUR website!
Odds of winning grand prize = 1/500
Odds of winning second prize = 2/500
Odds of winning third prize = 14/500
Odds of not winning any prize = 483/500

You must also remember that it costs $7 for the ticket, so if you win the $1000 grand prize (for example), you're really only winning $993. Same goes for any of the prizes.

1/500 * 993 = 993/500
2/500 * 193 = 386/500
14/500 * 3 = 42/500
483/500 * -7 = -3381/500

993/500 + 386/500 + 42/500 - 3381/500
= -1960/500
= -98/25
= -$3.92
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
E(x)=sum x*p(x)
=(1000-7)(1/500)+(200-7)(2/500)+(10-7)(14/500)-7(483/500), because $7 to play in the first place has to come out of the winning.
=993/500+386/500+42/500-3381/500
=-1960/500
=-$3.92 (loss)
Answer by ikleyn(52777)   (Show Source): You can put this solution on YOUR website!
.

The expected value for your profit is - 7 = - 7 = - 7 = 3.08 - 7 = -3.92 dollars per game. In other words, be ready to lose $3.92 in average, if you play many times this game, buying every time 1 ticket from 500.

Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

You have received three responses, all showing how to find the expected value based on the formal definition of expected value.

For many basic expected value problems like this, there is an easier way to find the expected value.

To the people buying the tickets, the total cost is 500 times $7, or $3500.

The total value of the prizes is $1000, plus 2 times $200, plus 14 times $10, for a total of $1540.

The expected value for each ticket is the difference between the total payout and the total cost, divided by the number of tickets:

ANSWER: The expected profit from each ticket is -$3.92.

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