Question

An auto insurance company is implementing a new bonus system. In each month, if a policyholder does not have an accident, they will receive a cash-back bonus of 5 from the company. Among the 1000 policyholder of the auto insurance company, 400 are classified as low-risk drivers and 600 are classified as high-risk drivers. In each month, the probability of zero accidents for high-risk drivers is 0.80 and the probability of zero accidents for low-risk drivers is 0.90. Calculate the expected bonus payment from the company to the 1000 policyholders in one year.

Answer 1

Answer:

50,400

Explanation:

Using application of total expectation, E;

N= Number of policy holders who have zero accidents in one month

P= Probability

N|Low = 400

N|High=600

P|Low=0.9

P|High=0.8

Therefore E = (N|Low*P|Low)+(N|High*P|High)

E=(400*0.9)+(600*0.8)

E=360+480

E=840

Then Total bonus for the year B

B= E*12*5

B=840*12*5

B=50,400