Exercise 13 Page 866

We want to decide whether the company executives should invest in a new business opportunity. To do so, we will calculate the expected value of the amount of money the company will make. Let's recall the definition of expected value.

Expected Value
If $A$ is an action that includes outcomes $A_{1},$ $A_{2},$ $A_{3}, \dots$ and $Value (A_{n})$ is a quantitative value associated with each outcome, the expected value of $A$ is given by $Value (A) = P (A_{1}) \cdot Value (A_{1}) + P (A_{2}) \cdot Value (A_{2}) + \dots$

In other words, it is what we get, when we add up all products of the possible made money and their corresponding probabilities. Before we start calculating, let's convert the probabilities from percent to decimal notation for convenience.

	Distribution of Money Made
Money Made, $Value (A_{i})$	$- $ 25000$	$$ 0$ (break even)	$$ 40000$
Probability, $P (A_{i})$	$40 % = 0.4$	$25 % = 0.25$	$35 % = 0.35$

Now, we can calculate all the products of the profits and their probabilities.

	Distribution of Money Made
Money Made, $Value (A_{i})$	$- $ 25000$	$$ 0$ (break even)	$$ 40000$
Probability, $P (A_{i})$	$0.4$	$0.25$	$0.35$
$P (A_{i}) \cdot Value (A_{i})$	$0.4 \cdot (- $ 25000) = - $ 10000$	$0.25 \cdot $ 0 = $ 0$	$0.35 \cdot $ 40000 = $ 14000$

Finally, we can calculate the expected value by summing all values from the the last row. Let's do it!

Value (A) = - $ 10000 + $ 0 + $ 14000 = $ 4000

The expected value of money made in the new business opportunity is

$ 4000 .

We conclude that on average the company is expected to make

$ 4000 .

Therefore, since the expected value is positive, the company executives should decide to invest in the opportunity.