In a product liability case, a company can settie out of court for a loss of $$ \$ 350,000 $$, or go to trial, losing $$ \$ 1,200,000 $$ if found guilty and nothing if found not guilty. Lawyers for the company estimate the probability of a not-gulity verdict to be 0.8. Complete parts (a) through (b) below. a. What is the expected value of the amount the company can lose by taking the case to court? 240000 b. Should the company settie out of court? A. The company should settle out of court, since the amount it expects to gain by going to trial is more than the cost of setting out of court. B. The company should settle out of couit, since the amount it expects to lose by going to trial is more than the cost of setting out of court. C. The company should allow the case to go to trial, since the amount it expects to gain by going to trial is more than the cost of setting out of court. D. The company should allow the case to go to trial, since the amount it expects to lose by going to trial is less than the cost of setting out of court.

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**Step 1. Calculate the expected loss if the company goes to trial**

The company faces two outcomes at trial:

- Loss of $$ \$1{,}200{,}000 $$ if found guilty.
- Loss of $$ \$0 $$ if found not guilty.

The estimated probability of a not-guilty verdict is $$ 0.8 $$. Therefore, the probability of a guilty verdict is $$ 1 - 0.8 = 0.2 $$.

The expected value $$ E $$ of the loss at trial is:
$$
E = (0.2)(\$1{,}200{,}000) + (0.8)(\$0)
$$
$$
E = \$240{,}000 + \$0 = \$240{,}000
$$

**Step 2. Compare the expected trial loss to the settlement cost**

- Settlement cost: $$ \$350{,}000 $$
- Expected trial loss: $$ \$240{,}000 $$

Since $$ \$240{,}000 < \$350{,}000 $$, the company expects to lose less money by going to trial than by settling.

**Step 3. Answer the questions**

a. The expected value of the amount the company can lose by taking the case to trial is:
$$
\$240{,}000
$$

b. The company should not settle out of court since the expected loss at trial is less than the settlement cost. This corresponds to:

**D. The company should allow the case to go to trial, since the amount it expects to lose by going to trial is less than the cost of setting out of court.**
a. The expected loss by going to trial is \$240,000. b. The company should allow the case to go to trial because the expected loss (\$240,000) is less than the settlement cost (\$350,000).

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