In a procuct labillyy ease, a company can settle out of court for a loss of \( \$ 850,000 \), or go to trial, loang \( \$ 1,200,000 \) ir found gully and nothind II found not gully, Lawers for the company estimate the probabilly of a noigully vertict to be 0.8 , Complete pats (a) through (b) below. a. What is the expected value of the ancunt the company can lose by taking the case to coutr \( \$ \) \( \square \)

To calculate the expected value of the amount the company can lose by taking the case to court, we can use the formula for expected value, which considers both possible outcomes: a guilty verdict and a not guilty verdict. 1. **Guilty Verdict**: The company loses $1,200,000 with a probability of \( 0.2 \) (since the probability of a not guilty verdict is \( 0.8 \)). 2. **Not Guilty Verdict**: The company loses $0 with a probability of \( 0.8 \). So, the expected value (EV) can be calculated as follows: \[ EV = (Loss \, if \, guilty) \times (Probability \, of \, guilty) + (Loss \, if \, not \, guilty) \times (Probability \, of \, not \, guilty) \] \[ EV = (1,200,000 \times 0.2) + (0 \times 0.8) \] \[ EV = 240,000 + 0 = 240,000 \] Thus, the expected value of the amount the company can lose by going to court is \( \$240,000 \). Now, let's wrap it all up: The expected value of the amount the company can lose by taking the case to court is \( \$240,000 \).