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13995173783 · 2023年06月28日

没想明白

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!

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已采纳答案

李坏_品职助教 · 2023年06月29日

嗨,努力学习的PZer你好:


A∩Hc,这个c意思是补集。Hc等于全集减去H。


  1. 40% of policyholders who have only an auto policy will renew next year,这句话意思是那些“仅有”汽车保险而没有住房保险的人里面,有40%的人会续保。所以40%*P(A∩Hc)的意思是用40%乘以只买了汽车保险的人数比例。这个算的是那些只买汽车保险的人续保的比例。
  2. 同理,70%*P(Ac ∩H)是用70%乘以只买了住房保险的人数比例。这个算的是那些只买住房保险的人续保的比例。
  3. 最后,两个保险都买了的比例是P(A∩H),乘以80%。这个算的是既买了汽车保险又买了住房保险的人续保的比例。
  4. 以上123的概率相加就是续保的总比例。



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努力的时光都是限量版,加油!

13995173783 · 2023年06月29日

谢谢老师!

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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 画图法如何解答,是否更简便

2023-04-19 22:27 1 · 回答

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2023-03-14 11:31 2 · 回答