SOLUTION: The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $6 each and will sell 900 tickets. There is one $3,000 grand prize, three $20

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Question 1199875: The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $6 each and will sell 900 tickets. There is one $3,000 grand prize, three $200 second prizes, and thirteen $40 third prizes. You just bought a ticket. Find the expected value for your profit. Round to the nearest cent.
$_________
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52808) About Me  (Show Source):
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The expected profit is

    3000%2A%281%2F900%29+%2B+200%2A%283%2F900%29+%2B+40%2A%2813%2F900%29 - 6 = %283000+%2B+3%2A200+%2B+13%2A40%29%2F900 - 6 = 4120%2F900 - 6 = 4.5778 - 6 = -1.4222 = -1.42 dollars  (rounded).


ANSWER.  The expected profit is -1.42 dollars.  The sign "minus" means your loss.  

         Your negative profit is a masked form of your donation to raise money for scholarships.

Solved, with explanations.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


900 tickets are sold at $6 each; the total income for the student council is $5400.

The total value of the prizes is $3000 + 3($200) + 13($40) = $4120.

The average income per ticket is ($5400-$4120)/900 = $1.42 rounded to the nearest cent.

The average income per ticket for the council is the average loss (expected value) per ticket for the ticket buyers.

ANSWER: The expected value is a loss of $1.42

Using the formal definition of expected value....

%28%281%2F900%29%283000-6%29%2B%283%2F900%29%28200-6%29%2B%2813%2F900%29%2840-6%29%29 = -1.42 to 2 decimal places.