Question

Recognizing the risk of being sued, Modus is considering buying insurance to guard against the financial consequences of a potential lawsuit. The company’s best estimate is that there is a 1.5% chance of a serious failure of one of their test-kits, resulting in a lawsuit, over the next year. Andre Serrano estimates that in the case of such a serious failure a court is almost certain to find in favour of the patient, and—on average—to award the patient damages of about $1.25 million.

A: What is the expected value of taking this risk, and not buying insurance at all for the coming year? (Show your math.)

B: What is the expected value of buying, in this context, an insurance policy that costs $4,500 for the year, and that would cover up to $800,000 in damages in case of a lawsuit? (Show your math.)

Answer 1

solution A. thet x denote. the expected losslist) of the company over a law suit. x here com take two values. X=0, if no test kit fails. This is considered as a success. f *-412, 50.000; if a test kit fails. muis is considered as a failure Hannt It is also given that there is chance of 1.5% failere failile late. That is, P[Failuar): 1.5.15 -0.015: P(x = la50.000 P[Success) = 1-0.015-0.985.=P(x=0) Then, the expected value of x FE(X)= a.P6X:) 0.P(x=0)+ €1,250.000) P(x:1,250.000 (1,250,000 0.015 ے * I = -18,750. That is, on an average the comipany wiu loose $18.950 per test kit produced

No. Date : an B. If the company decides to levy insurance cover $800.000 for Policy $4500, เช 0 q cost Now, P[Failure ga kit] =0.015 and P[No failure) = 0.985. Expected Value = P[Failure).es claimed a üsulance +P (Rofailure) efforencium paid) = 0.015) 800,000 +0.985 (-4500) 12.000 4432.5 7567.5. That is, if an insurance to bought, the company's gains will be on an average $7567.5.