2-16 38 have life policies, 29 have health policies and 21 have both. How many c

Question

2-16 38 have life policies, 29 have health policies and 21 have both. How many clients does he have? (recall Venn diagrams) Insurance: An insurance agent sells two types of insurance, life and health. Of his clients Insurance: An insurance company divides its policyholders into low-risk and high-risk 3-40 classes. For the year, of those in the low risk class, 80% had no claims, 15% had one claim, and 5% 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. (recall conditional probability) If a policy holder has no claims in the years, 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? A) B)

Explanation / Answer

Question 2.16

Here we know that all clients must have at least one of the 2 policies, therefore the required number of people here with at least one of the 2 types of policies is computed using the law of addition of probability is computed as:

n ( life or health ) = n( life ) + n( health ) - n( life and health )

n ( life or health ) = 38 + 29 - 21 = 46

Therefore the insurance agent has exactly 46 clients here.

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