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🌊Yuri🌊 · 2022年12月01日

NO.PZ2015120604000076

问题如下:


According to the above table, and we are informed that the performance of next day is good, what is the probability of today's performance is good?

选项:

A.

0.74.

B.

0.28.

C.

0.67.

解释:

C is correct.

We can use Bayes' formula to solve this problem.

A: today's performance is good.

B: next day's performance is good.

P(A|B)=P(B|A)*P(A)/P(B)=0.7×0.4/(0.4×0.7+0.2×0.3+0.4×0.2)

P(B|A)*P(A)=0.7×0.4=0.28

P(B)=0.4×0.7+0.2×0.3+0.4×0.2=0.42

P(A|B)=0.67

老师,这个式子完全没看懂,麻烦解释一下每一步。谢谢

1 个答案
已采纳答案

星星_品职助教 · 2022年12月02日

同学你好,

本题的问题为“the performance of next day is good, what is the probability of today's performance is good”,即要计算的是P(today good | next day good)。

根据贝叶斯公式的形式: P(A|B)=P(B|A) / P(B) × P(A),可知P(today good | next day good)= P(next day good | today good ) / P(next day good) × P(today good)

其中,P(next day good)这一项不是已知的,观察图表,发现有三种情况可以达到P(next day good):

1)P(next day good and today good),这种情况的概率为0.4×0.7

2)P(next day good and today neutral),这种情况的概率为0.2×0.3

3)P(next day good and today poor),这种情况的概率为0.4×0.2

所以P(next day good)的全概率即为这三种情况的加和,也就是0.4×0.7+0.2×0.3+0.4×0.2=0.42。

代入前述的公式,可得=P(today good | next day good)=0.70 / 0.42 ×0.40=0.6666

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