The complete question is as follows:
Tom wants to avoid any accidents on the work floor of his factory. If an accident does occur, it would cost him $500,000 in damages. Installing safety equipment would decrease the probability of an accident occurring from 20% to 10%. However, the equipment costs $20,000 to install. Would Tom install the safety equipment?
a. Yes because it costs him less than its worth
b. Yes because it cost him more than its worth
c. No because it costs him more than its worth
d. No because it costs him less than its worth
Answer: a. Yes, because it costs him less than its worth .
We arrive at the answer as follows:
Damages if the accident occur = -$500,000
We use a negative sign before 500,000 since it represents a loss to the company.
Probability of accident before installing safety equipment = 20%
Probability of accident after installing safety equipment = 10%
We can calculate expected value of loss before and after installing the equipment with the following formula:
So,
Next, we calculate the benefit from installing safety equipment as follows:
Benefit of safety equipment = + $50,000
Cost of safety equipment = $20,000
Since the net benefit of installing the safety equipment is positive, Tom will install the safety equipment.