A nonprofit organization sells chances for a $40,000 automobile at $125 per ticket. It sells 2,000 tickets and offers four prizes, summarized in the table that follows. What are the expected winnings (or loss) for each ticket?

Question

Quizplus · Accepted Answer

To find the expected winnings (or loss), we need to first find the probability of each outcome and then multiply it by the value of that outcome.

The probability of winning the automobile is 1/2000, so the value of that outcome is $40,000 and the expected value of that outcome is (1/2000) x $40,000 = $20.

The probability of winning the second prize is 1/1000, so the value of that outcome is $4,000 and the expected value of that outcome is (1/1000) x $4,000 = $4.

The probability of winning the third prize is 1/500, so the value of that outcome is $1,000 and the expected value of that outcome is (1/500) x $1,000 = $2.

The probability of winning the fourth prize is 1/250, so the value of that outcome is $500 and the expected value of that outcome is (1/250) x $500 = $2.

Now we can calculate the expected winnings (or loss) for each ticket: 
Expected winnings = (probability of winning automobile x expected value of automobile) + (probability of winning second prize x expected value of second prize) + (probability of winning third prize x expected value of third prize) + (probability of winning fourth prize x expected value of fourth prize) - (cost of ticket) 
Expected winnings = [(1/2000) x $40,000] + [(1/1000) x $4,000] + [(1/500) x $1,000] + [(1/250) x $500] - $125 
Expected winnings = $20 + $4 + $2 + $2 - $125 
Expected winnings = -$97

Therefore, the expected winnings (or loss) for each ticket is -$97.

Among the given choices, the best one is B as it correctly calculates the expected loss for a person.

A Nonprofit Organization Sells Chances for a $40,000 Automobile at $125