SOLUTION: A lottery consists of one $2000 winner, three $500 winners, and ten $100 winners. A total of 1000 tickets are sold for $10 each. Find the expected winnings for a person purchasing
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Question 696327: A lottery consists of one $2000 winner, three $500 winners, and ten $100 winners. A total of 1000 tickets are sold for $10 each. Find the expected winnings for a person purchasing one ticket.
Answer by Positive_EV(69) (Show Source): You can put this solution on YOUR website!
The expected value is equal to the sum of the products of each outcome's gain/loss and its associated probability. The probabilities of each outcome are:
$2000: 1/1000 = .001
$500: 3/1000 = .003
$100: 10/1000 = .01
-$10: 1 (Everyone who buys a ticket loses $10 to buy the ticket. Thus, by entering the raffle this event will always happen. It can happen in conjunction with winning any of the winning results, also -- so the $2000 prize winner will actually win $1990, not $2000.)
The expected value is:
2000*(.001) + 500*(.003) + 100*(.01) - 10*1 = -5.5
A person playing this raffle can expect to lose $5.50 for every ticket they buy.
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