Question 1195253: MD has a new type of scratch-off ticket for $500 to win one of:
10 prizes of $700
2 runner-up prizes of $3,000
1 grand prize of $600,000
Once they’ve sold 5,000 tickets, they will select the winning tickets.
What is the expected value?
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
The question is presumably the expected value OF ONE TICKET....
(1) Using the formal definition of expected value....
Cost: $500
10/5000 chance of winning $700
2/5000 chance of winning $3000
1/5000 chance of winning $600,000
Expected value:
ANSWER: -377.4; or a loss of $377.40
(2) Using a less formal common sense method (which uses the same calculations, though in a different order)....
Total payout: 10($700)+2($3000)+1($600,000) = $613,000
Total cost of the 500 tickets: 5000($500) = $2,500,000
payout minus cost: -$1,887,000
expected value per ticket: (-$1,887,000)/5000 = -$377.40
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