A business has an opportunity to invest 35 dollars comma 000 If the investment is a success, the business earns a profit of 150 dollars comma 000 Otherwise, the investment will result in a total loss of all monies. If the investment has 0 point 2 7 chance of success, which equation correctly models the expected value of this investment?
Answer
A
150 comma 000 minus 0 point 7 3 times open paren 35 comma 000 close paren is equal to cap e times cap x
B
0 point 2 7 times open paren 150 comma 000 close paren plus 0 point 7 3 times open paren negative 35 comma 000 close paren is equal to cap e times cap x
C
0 point 2 7 times open paren 150 comma 000 minus 35 comma 000 close paren is equal to cap e times cap x
D
0 point 2 7 times open paren 115 comma 000 close paren plus 0 point 7 3 times open paren negative 35 comma 000 close paren is equal to cap e times cap x
Explanation
Expected value is the sum of each outcome multiplied by its probability. Success has probability 0.27 and earns a profit of $150,000; failure has probability 1 − 0.27 = 0.73 and loses the $35,000 investment. So the equation is 0.27($150,000) + 0.73(−$35,000) = E(X), which is choice B.
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