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华赞 · 2023年04月19日

可否用画图法

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

画图法如何解答,是否更简便

1 个答案

品职答疑小助手雍 · 2023年04月19日

同学你好,画图法也行,不过只是方便理解而已。贝叶斯的这类题,其实主要就是英语阅读理解,读懂了自然后会了。

图中10个各自,不同颜色从上到下对应的就是只买了车险的50%,车险房险都有的20%,只有房险的30%。

每个部分乘以他们续约的概率40%,80%,70%就行了。

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NO.PZ2022062760000025 问题如下 insurancompany estimates th40% of policyholrs who have only auto poliwill renew next year, an70% of policyholrs who have only a homeowner poliwill renew next year. The company estimates th80% of policyholrs who have both auto ana homeowner poliwill renew least one of those policies next year. Company recor show th70% of policyholrs have auto policy, 50% of policyholrs have a homeowner policy, an20% of policyholrs have both auto ana homeowner policy. Using the company’s estimates, whis the percentage of policyholrs thwill renew least one polinext year? A.29% B.41% C.53% 57% 中文解析先定义AB事件A = event tha policyholr hauto poliH = event tha policyholr ha homeowner poli通过已知条件可得P(A∩H) = 0.20 P(A∩H= P(- 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∩H+ 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!

2023-06-28 23:44 1 · 回答

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2023-03-14 11:31 2 · 回答