can someone please help me solve this problem? An insurance company divides its
ID: 3333539 • Letter: C
Question
can someone please help me solve this problem? An insurance company divides its policyholders into low-risk and high-risk classes. For the year, of those in the low-risk class, 80% had no claims, 15% had one claim, and 500 had 2 claims. Of those in the high-risk class, 50% had no claims, 30% had one claim, and 20% had two claims. Of the policyholders, 60% were in the low-risk class and 40% in the high-risk class. (a) If a policyholder had no claims in the year, what is the probability that he is in the low-risk class? If a policyholder had two claims in the year, what is the probability that he is in the high-risk class? (b)Explanation / Answer
a)
Required probability = P( the policyholder is in the low-risk class given he had no claims in the year )
= P( the policyholder is in the low-risk class and he had no claims in the year ) / P(the policyholder had no claims in the year)
Now, P( the policyholder is in the low-risk class and he had no claims in the year ) = (0.60)(0.80) = 0.48
and,P(the policyholder had no claims in the year) = P(the policyholder had no claims in the year and he belongs to low-risk class) + P(the policyholder had no claims in the year and he belongs to high-risk class)
= (0.60)(0.80) + (0.40)(0.50) = 0.68
Hence, Required probability = 0.48 / 0.68 = 12 / 17 = 0.7059
b)
Required probability = P( the policyholder is in the high-risk class given he had two claims in the year )
= P( the policyholder is in the high-risk class and he had two claims in the year ) / P(the policyholder had two claims in the year)
Now, P( the policyholder is in the high-risk class and he had two claims in the year ) = (0.40)(0.20) = 0.08
and,P(the policyholder had two claims in the year) = P(the policyholder had two claims in the year and he belongs to low-risk class) + P(the policyholder had two claims in the year and he belongs to high-risk class)
= (0.60)(0.05) + (0.40)(0.20) = 0.11
Hence, Required probability = 0.08 / 0.11 = 8 / 11 = 0.7273
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.