问题如下：
Company A is a crude oil supplier. As an analyst, you should judge whether Company A will have new development by estimating Company A's largest customer B company will whether increase the order volume or not. You estimate that the probability that Company B will increase the order volume is 30%. If Company B does increase the order volume, Company A will have a new development probability of 80%. If Company B does not increase the order volume, then Company A will have a new development probability of only 10%. After that, you discovered that crude oil supplier company A has started a new development. Under this condition, what is the probability that you estimate the company B to increase the order volume?
选项：
A. 18.59%.
B. 22.58%.
C. 77.42%.
D. 22.58%.
解释：
C is correct.
考点：Bayes' Formula
解析：涉及到贝叶斯公式的题目，首先要定义事件。
定义事件：B1——Company B will increase the order volume，B2——Company B will not increase the order volume，
A1——Company A will start a new development，
A2——Company A will not start a new development
根据已知条件：P(B1)=30%，P(A1|B1)=80%，P(A1|B2)=10%。求的是P(B1|A1)。
根据贝叶斯公式，P(B1|A1)=P(A1B1)/P(A1)，所以接下来分别求P(A1B1)和P(A1)。
由P(B1)=30%，得到P(B2)=70%。
P(A1B1)=P(A1|B1)*P(B1)=80%*30%=0.24
P(A1B2)=P(A1|B2)*P(B2)=10%*70%=0.07
所以P(A1)=P(A1B1)+P(A1B2)=0.31
所以P(B1|A1)=P(A1B1)/P(A1)=0.24/0.31=77.42%
老师这道题能否详细讲解一下
