Respuesta :
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 Â
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:
[tex] Expected Value of loss = Loss * Probability of loss [/tex]
So,
[tex] Expected Value of loss before safety equipment = -$100000 (-500000 *0.2) [/tex]
[tex] Expected value of loss after safety equipment = -$50,000 (-500000 * 0.10) [/tex]
Next, we calculate the benefit from installing safety equipment as follows:
[tex] Benefit of safety equipment = Expected value of loss after safety equipment - Expected value of loss before safety equipment. [/tex]
[tex] Benefit of safety equipment = -50000 - (-100000) [/tex]
[tex] Benefit of safety equipment = -50000 + 100000 [/tex]
Benefit of safety equipment = + $50,000
Cost of safety equipment = $20,000
[tex] Net benefit of safety equipment = Benefit from safety equipment - Cost of safety equipment [/tex]
[tex] Net benefit = $30,000 ($50,000 - $20,000) Â [/tex]
Since the net benefit of installing the safety equipment is positive, Tom will install the safety equipment.
