🌊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.
老师，这个式子完全没看懂，麻烦解释一下每一步。谢谢
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
NO.PZ2015120604000076问题如下 Accorng to the above table, anwe are informeththe performanof next y is goo whis the probability of toy's performanis goo A.0.74.B.0.28.C.0.67. C is correct.We cuse Bayes' formula to solve this problem.toy's performanis goonext y's performanis gooP(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=0.28P(B)=0.4×0.7+0.2×0.3+0.4×0.2=0.42P(A|B)=0.67 我的理解贝叶斯公式是P（A｜B）=P（B｜A）*P（A）/P（B），P（B｜A）=0.4*0.7，P（B）=0.4*0.7+0.2*0.3+0.4*0.2=0.42，P（A）=0.4，但是这样算下来跟答案不一样，是不是P（A）错了？
NO.PZ2015120604000076 问题如下 Accorng to the above table, anwe are informeththe performanof next y is goo whis the probability of toy's performanis goo A.0.74. B.0.28. C.0.67. C is correct.We cuse Bayes' formula to solve this problem.toy's performanis goonext y's performanis gooP(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=0.28P(B)=0.4×0.7+0.2×0.3+0.4×0.2=0.42P(A|B)=0.67 这个题目有问题吧？题目的意图是想考察条件概率，但是问法并不是，问的就是一个独立事件的概率。
NO.PZ2015120604000076 问题如下 Accorng to the above table, anwe are informeththe performanof next y is goo whis the probability of toy's performanis goo A.0.74. B.0.28. C.0.67. C is correct.We cuse Bayes' formula to solve this problem.toy's performanis goonext y's performanis gooP(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=0.28P(B)=0.4×0.7+0.2×0.3+0.4×0.2=0.42P(A|B)=0.67 这个题用贝叶斯公式怎么画图啊
NO.PZ2015120604000076 问题如下 Accorng to the above table, anwe are informeththe performanof next y is goo whis the probability of toy's performanis goo A.0.74. B.0.28. C.0.67. C is correct.We cuse Bayes' formula to solve this problem.toy's performanis goonext y's performanis gooP(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=0.28P(B)=0.4×0.7+0.2×0.3+0.4×0.2=0.42P(A|B)=0.67 如题
