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Question 4 • Mathematics III

A math club is researching a golf tournament fund-raiser. It will cost 1 dollars comma 000 to host the tournament. If it rains, the club will lose the investment. If it is sunny, it is expected that the club will collect 4 dollars comma 500 from the participants. If the chance of rain is 20 percent , what is the expected value for the tournament?

Answer
A
3 dollars comma 400
B
negative 200 dollars
C
2 dollars comma 600
D
negative 800 dollars

Explanation

If it rains, the club loses its $1,000 investment, so the net result is −$1,000. If it is sunny, the $4,500 collected minus the $1,000 cost gives a net of $3,500. The expected value is 0.20(−$1,000) + 0.80($3,500) = −$200 + $2,800 = $2,600, so the expected value is $2,600.

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