# Calculate the probability that losses will be 40000 or below

The risk manager for a factory has been studying the pattern of annual property losses over past years and has arrived the following the probability distribution:

Annual cost of losses                                                                                         probability

0-8000                                                                                                                                   0.15

8001-16000                                                                                                                          0.3

16001-40000                                                                                                                       0.25

40001-80000                                                                                                                       0.15

80001-160000                                                                                                                     0.08

160001-400000                                                                                                   0.05

40001-800000                                                                                                                     0.02.

An insurance company has quoted an insurance premium of 60000 to cover the risk

Required (making the necessary assumptions and showing all workings)

a)Calculate the probability that losses will be 40000 or below

b)Calculate the expected \$ loss per year

c)Calculate on the basis of expected monetary value (EMV), how much would be saved if the insurance cover was not purchased

d)Now assume that an insurance policy with a 80000 deductible/excess can be purchased for an annual insurance premium of 20000 (ie the factory owner pays the first 80000 of total annual losses) calculate the expected total cost of protection under this arrangement

e)Explain the factors which would influence the choice between 1) full retention of the risk 2) the deductible arrangement and 3) full insurance

(100 words)

f)Explain any factors, other than those mentioned in the question, which could also influence the decisions

(100 words)