a business has an opportunity to invest $35,000. if the investment is a success, the business earns a profit…

a business has an opportunity to invest $35,000. if the investment is a success, the business earns a profit of $150,000. otherwise, the investment will result in a total loss of all monies. if the investment has 0.27 chance of success, which equation correctly models the expected value of this investment?\n0.27(150,000) + 0.73(-35,000) = e(x)\n150,000 - 0.73(35,000) = e(x)\n0.27(150,000 - 35,000) = e(x)\n0.27(115,000) + 0.73(-35,000) = e(x)

a business has an opportunity to invest $35,000. if the investment is a success, the business earns a profit of $150,000. otherwise, the investment will result in a total loss of all monies. if the investment has 0.27 chance of success, which equation correctly models the expected value of this investment?\n0.27(150,000) + 0.73(-35,000) = e(x)\n150,000 - 0.73(35,000) = e(x)\n0.27(150,000 - 35,000) = e(x)\n0.27(115,000) + 0.73(-35,000) = e(x)

Answer

Explanation:

Step1: Recall expected - value formula

The formula for the expected value $E(X)$ of a discrete - random variable is $E(X)=\sum_{i}x_ip_i$, where $x_i$ are the possible values and $p_i$ are their corresponding probabilities.

Step2: Identify the two possible outcomes and their probabilities

The probability of success $p_1 = 0.27$. In case of success, the net gain is the profit minus the investment. The profit is $$150,000$ and the investment is $$35,000$, so the net gain $x_1=150000 - 35000=115000$. The probability of failure $p_2=1 - 0.27 = 0.73$. In case of failure, the net gain is $x_2=- 35000$ (a loss of the entire investment).

Step3: Calculate the expected value

Using the expected - value formula $E(X)=p_1x_1 + p_2x_2$, we substitute $p_1 = 0.27$, $x_1 = 115000$, $p_2 = 0.73$, and $x_2=-35000$. So $E(X)=0.27(115000)+0.73(-35000)$.

Answer:

D. $0.27(115,000)+0.73(-35,000)=E(X)$