NO.PZ2023091601000003
问题如下：
An
insurance company estimates that 40% of policyholders who have only an auto
policy will renew next year, and 60% of policyholders who have only a homeowner
policy will renew next year. The company estimates that 80% of policyholders
who have both an auto and a homeowner policy will renew at least one of those
policies next year. Company records show that 65% of policyholders have an auto
policy, 50% of policyholders have a homeowner policy, and 15% of policyholders
have both an auto and a homeowner policy. Using the company's estimates, what
is the percentage of policyholders that will renew at least one policy next
year?
选项：
A.20%
B.29%
C.41%
D.53%
解释：
Let:
A = event that a
policyholder has an auto policy
H = event that a
policyholder has a homeowners policy
Then, based on the
information given:
P (A and H) = 0.15
P (A and Hc) = P (A) – P (A
and H) = 0.65 – 0.15 = 0.5
P (AC and H) = P (H) – P
(A and H) = 0.5 – 0.15 = 0.35
Therefore, the
proportion of policyholders that will renew at least one policy is shown below:
0.4
* P (A and Hc) + 0.6 * P (Ac and H) + 0.8 * P (A and H) = 0.4 * 0.5 + 0.6 *
0.35 + 0.8 * 0.15 = 0.53
如题
