Question

You are the Claims Manager for a large auto insurance firm. You know the following facts: • 25% of your policy-holders are younger (age 16-34). Within this group, 55% are men and 45% are women. Only some of these policy holders make an accident claim. The men have a 10% probability of making a claim, while the women have a 5% probability of making a claim. • 50% of your policy-holders are middle-aged (ages 35-59). Of these, 50% are men and 50% are women. Only some of these policy holders make an accident claim. The men and women within this age group have 4% and 3% probabilities of making a claim, respectively. • 25% of your policy-holders are older (ages 60 and above). Of these, 55% are women and 45% are men. Only some of these policy holders make an accident claim. The men and women each have a 2% probability of making a claim.

(a) What is the probability that a policy-holder who makes a claim is in the “16-34” age group?

(b) What is the probability that a policy-holder who does not make a claim is in the “60 and above” age category?

Answer 1

SN	Age group	Men	Women	total
1	16-34	0.55     (0.10)	0.45      (0.05)	0.25
2	35--59	0.5      (0.04)	0.5.      ( 0.03)	0.5
3	60--above	0.45      (0.02)	0.55        (0.02)	0.25
				total
	claim 1	0.055	0.0225	0.0775	0.25	0.019375
	claim 2	0.02	0.015	0.035	0.5	0.0175
	claim3	0.009	0.011	0.02	0.25	0.005
						0.041875
	P(claim)=	0.25*0.0775+0.5*0.035+0.25*0.02
	P(claim)=	0.041875
	The probability that a policy-holder who
	makes a claim is in the “16-34” age group =	0.019375/0.041875
				0.462686567
SN	Age group	Men	not claim	Women	not claim	total
1	16-34	0.55	0.9	0.45	0.95	0.25
2	35--59	0.5	0.96	0.5	0.97	0.5
3	60--above	0.45	0.98	0.55	0.98	0.25
				total
	no claim1	0.495	0.4275	0.9225	0.25	0.230625
	no claim2	0.48	0.485	0.965	0.5	0.4825
	no claim3	0.441	0.539	0.98	0.25	0.245
						0.958125
	P( no claim)=	0.25*0.9225+0.5*0.965+0.25*0.98
	P( no claim)=	0.958125
	The probability that a policy-holder who does not
	make a claim is in the “60 and above” age category =	0.245/.958125
					0.255707763