Question

don is considering bringing a lawsuit against the dummote company. his lawyer estimates that there is a 60% chance don will make $60,000, a 10% chance don will break even, and a 30% chance they will lose the case and don will need to pay $30,000 in legal fees. estimate dons expected gain or loss if he proceeds with the lawsuit. select the correct choice below and, if necessary, fill in the answer box within your choice. a. don has an expected loss of $ b. don has an expected gain of $ c. don has neither an expected gain nor expected loss

Explanation:

Step1: Calculate the expected value

The formula for expected value \(E(X)=\sum_{i = 1}^{n}x_ip_i\), where \(x_i\) is the value of the \(i\) - th outcome and \(p_i\) is the probability of the \(i\) - th outcome.
Let \(x_1 = 60000\), \(p_1=0.6\); \(x_2 = 0\), \(p_2 = 0.1\); \(x_3=- 30000\), \(p_3 = 0.3\)

$$
LATEXBLOCK0
$$

Step2: Simplify the expression

$$ E(X)=36000-9000=27000 $$

Since \(E(X)=27000>0\), it is a gain.

Answer:

B. Don has an expected gain of \(\$27000\)