In a product liability case, a company can setile out of court for a loss of \( \$ 350,000 \), or go to trial, losing \( \$ 1,200,000 \) If found gully and nothing If found not gullty. Lawers for the company estimate the probability of a nol-gullity verdict to be 0.8. Complete parts (b) through (b) below. a. What is the expected value of the amount the company can lose by taking the case to court? \( \$ \) \( \square \)

To calculate the expected value of the amount the company can lose by taking the case to court, we can break it down based on the probabilities and outcomes. If the company goes to trial, there are two possible outcomes: 1. They are found guilty with a probability of \(0.2\): In this case, they lose \( \$1,200,000 \). 2. They are found not guilty with a probability of \(0.8\): In this case, they lose \( \$0 \). Using this information, we can calculate the expected loss: \[ \text{Expected Loss} = (Probability_{guilty} \times Amount_{guilty}) + (Probability_{not\_guilty} \times Amount_{not\_guilty}) \] \[ \text{Expected Loss} = (0.2 \times -1,200,000) + (0.8 \times 0) \] \[ \text{Expected Loss} = -240,000 + 0 = -240,000 \] So, the expected value of the amount the company can lose by taking the case to court is \( -\$240,000 \). Now, here is some additional relevant knowledge: When companies face product liability cases, they often weigh the cost of settlement versus the risk of a trial. Settling may seem more appealing due to lower financial exposure and the avoidance of unpredictable jury decisions. Companies with a solid understanding of probability can make more informed choices, just like in our scenario—where deciding whether to settle or go to trial can significantly impact their financial health. Consider this scenario: if the company opts for trial, they might hire a legal team that specializes in product liability defense. Engaging experienced lawyers who understand the intricacies of the law can make a substantial difference. Still, lending a portion of their success to the unpredictable nature of trials remains a risk! Remember, the right choice isn't just about the math; it's also about the overall risk strategy of the company!