Question

need to solve it on excel as soon as possible

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

Three Buildings A,B and C
For Each Building:
Probability of Loss 0.01 0.0099
Probability of No Loss 0.99 0.0099
Expected Loss to Insured $120000*0.01= $1,200
SAMPLE SPACE
p A B=A*p D=A-3600 E=D^2 F=p*D
OCCURANCE OF EVENT CALCULATION Probability Amount of Loss Expected Loss(Probability*Amount) Deviation from Expected Deviation Squared Probability*Deviation Squared
Loss to One Building Loss to A and No loss to B&C (0.01*0.99*0.99) 0.009801 $120,000 $1,176 $116,400 $13,548,960,000 $132,793,357
Loss to One Building Loss to B and No loss to A&C (0.01*0.99*0.99) 0.009801 $120,000 $1,176 $116,400 $13,548,960,000 $132,793,357
Loss to One Building Loss to C and No loss to A&B (0.01*0.99*0.99) 0.009801 $120,000 $1,176 $116,400 $13,548,960,000 $132,793,357
Loss to Two Buildings Loss to A&B and No loss to C (0.01*0.01*0.99) 0.000099 $240,000 $24 $236,400 $55,884,960,000 $5,532,611
Loss to Two Buildings Loss to A&C and No loss to B (0.01*0.01*0.99) 0.000099 $240,000 $24 $236,400 $55,884,960,000 $5,532,611
Loss to Two Buildings Loss to B&C and No loss to A (0.01*0.01*0.99) 0.000099 $240,000 $24 $236,400 $55,884,960,000 $5,532,611
Loss to Three Buildings Loss to A, B&C (0.01*0.01*0.01) 0.000001 $360,000 $0.36 $356,400 $127,020,960,000 $127,021
No Loss No Loss to A,B and C (0.99*0.99*0.99) 0.970299 $0 $0 ($3,600) $12,960,000 $12,575,075
SUM $3,600 SUM $427,680,000
EXPECTED LOSS TO INSURER $3,600
VARIANCE OF LOSS TO INSURER $427,680,000
Standard Deviation=Square Root (Variance)
RISK=Standard Deviation of Loss $20,680 (SQRT(427680000)