Question

An automobile manufacturer designed a car with the gas tank in the rear the effect of which was to create a one-in-four risk of fire from rear-end collisions. An alternate design would have reduced the risk of fire to one out of twenty collisions, but at a cost of $10 per car. Suppose that one out of five thousand cars are rear-ended at least once during their lifetime, and the average damage from a fire is $100,000. Use the Hand rule to determine if the manufacturer should be held negligent for failing to use the alternate design

Answer 1

Let us consider both designs and the relevant costs for a car.

Gas tank at rear.

Probability of rear end collision,

Probability of fire in case of rear end collision,

Therefore, probability of fire,

Expected loss,

That is, we expect a loss of $5 in case the gas tank is kept at rear.

Alternate Design

Extra costs =$10

The extra costs in the alternate design is $10 which is more than the expected loss from keeping gas tank at the rear. Hence, manufacturer cannot be held negligent for not using the alternate design.