Question

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)

Please Solve As soon as
Solve quickly I get you thumbs up directly
Thank's
Abdul-Rahim Taysir

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)