SOLUTION: The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $7 each and will sell 800 tickets. There is one $1,000 grand prize, four $500

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Question 1199756: The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $7 each and will sell 800 tickets. There is one $1,000 grand prize, four $500 second prizes, and fourteen $30 third prizes. You just bought a ticket. Find the expected value for your profit. Round to the nearest cent.
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Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


(1) The solution using the formal definition of expected value -- which is probably how you are supposed to solve the problem....

(1/800) chance of winning $1000; (4/800) chance of winning $500; (14/800) chance of winning $30:

%281%2F800%291000%2B%284%2F800%29500%2B%2814%2F800%2930
1000%2F800%2B2000%2F800%2B420%2F800
3420%2F800
4.275

Your expected winnings are $4.27, rounded to the nearest cent. Since the ticket cost $7, your expected profit is $4.27-$7.00 = -$2.73.

ANSWER: -$2.73

(2) A much simpler solution, informally....

The total prize money is $1000 + 4($500) + 14($30) = $1000 + $2000 + $240 = $3420
The average prize money per ticket is $3420/800 = $4.275 or $4.27
The average profit per ticket is $4.27 - $7.00 = -$2.73