Question: A car manufacturer is considering how many safety devices to install on a new car. The devices function independently and each one works with probability .9. Furthermore, they are connected "in parallel" so that if any one of the devices installed works the car will be safe. How-ever, if they all fail the car will explode just as it is driven off the dealer's lot! The ensuing lawsuit (initiated by the estate for the unfortunate customer) will cost the manufacturer $1,000,000 every time this occurs. On the other hand, each safety device costs $100 to install. The car itself (without safety devices) costs $5,000 to build. Assume that the manufacturer will sell N (a given) cars at $10,000 each no matter how many safety devices are installed and that the firm wants to maximize the expectation of its profits.
a. How many safety devices will be installed in each car?
b. Given the answer to part (a), what will be the expectation and variance of their profits?
c. If N = 20, what is the probability that the firm will have at least one fatality arising from their choice of the number of safety devices installed?
d. The existence of the deliberations is leaked to Hard Copy and their next show claims "Auto Firm Puts Value on Human Life." Did the firm put a value on human life, and, if so, is this in and of itself worthy of condemnation?