NO.PZ2022062760000025
问题如下：
An insurance company estimates that 40% of policyholders who have only an auto policy will renew next year,
and 70% 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 70% of policyholders have an auto policy, 50% of policyholders
have a homeowner policy, and 20% 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.29%
B.41%
C.53%
D.57%
解释：
中文解析：
先定义AB事件：
A = event that a policyholder has an auto policy
H = event that a policyholder has a homeowner policy
通过已知条件可得：
P(A∩H) = 0.20
P(A∩Hc ) = P(A) - P(A∩H) = 0.70 - 0.20 = 0.50
P(Ac∩H) = P(H) - P(A∩H) = 0.50 - 0.20 = 0.30
即可得出:
0.40 * P(A∩Hc ) + 0.70 * P(Ac∩H) + 0.80 * P(A∩H)
= 0.40 * 0.50 + 0.70 * 0.30 + 0.80 * 0.20
= 0.57
看不明白A交H后面的那个符号是什么意思
本题目为什么不是直接计算A并B呢？P（A）*40%+P（B）*70%-P（AB）*20%=0.7*0.4+0.5*0.7-0.2*0.8
请老师解答，谢谢！
