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贝叶斯公式

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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：

20%

29%

41%

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

请问这道题用贝叶斯怎么画图

嗨，努力学习的PZer你好：

这道题好像不太好用画图法，如果一定要用图形的话，你可以想象一个饼图，里面只买了车险的50%，车险房险都有的15%，只有房险的35%。每个部分乘以他们续约的概率40%，80%，60%，最后再相加就行了。

详细一点的解释：

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。

同理，60%*P(Ac ∩H)是用60%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。

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。

以上123的概率相加就是续保的总比例。

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贝叶斯公式

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