Question

Due date is today after 3 hours

Assume that three business owners each own an identical storage building valued at $120,000.

Assume that there is a 1% chance in any year each building will be destroyed by a peril (fire), and that a loss to any of the buildings is an independent event. Assuming that:

(first case ) Fire events are independent of each other

(second case) Each building faces the same types of risks and environmental conditions.

Given that, solve the below questions for each case:

1. Use the compound probability of independent events law to find the sample space of the probability of each possible event

2. Find the annual expected loss for each of the insureds.

3. Find the risk of incurrence of losses (Std dev)

Answer 1

Answer:

Given Data

1) Use the compound probability of independent events law to find the sample space of the probability of each possible event.

Possible events:

Probability of no fire	99%
Probability of fire	1%
Possible Outcomes	Probability
Neither building is destroyed	=0.99*0.99*0.99	97.0299%
First building destroyed , Other two building no loss	=0.01 * 0.99 * 0.99	0.9801%
Second building destroyed , Other two building no loss	=0.01*0.99*0.99	0.9801%
Third building destroyed , Other two building no loss	=0.01*0.99*0.99	0.9801%
First and second building destroyed , third building no loss	=0.01 * 0.01 * 0.99	0.0099%
First and third building destroyed , second building no loss	=0.01*0.01*0.99	0.0099%
Second and third building destroyed , first building no loss	=0.01*0.01*0.99	0.0099%
All three buildings face loss	=0.01*0.01*0.01	0.0001%

2)   Find the annual expected loss for each of the insureds.

Expected loss = 0.99 * 0 + 0.01 * 120000

= 0 + 1200

= $1,200

3) Find the risk of incurrence of losses (Std dev).

Risk of incurrence of losses

= 11939.8492453

= $ 11,939.85

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