统计学的概率题P(A)=13/25 P(B)=9/25 条件概率P(A/B)=5/9 问：P(A and B) P(B/A) P(A or B or both) P(A or B or not both) P(A'/B') P(A/B') 另外,P(A U B) 和P(A ^ B) ^为倒立的U
问题描述：
统计学的概率题
P(A)=13/25 P(B)=9/25 条件概率P(A/B)=5/9
问：P(A and B) P(B/A) P(A or B or both) P(A or B or not both)
P(A'/B') P(A/B')
另外,P(A U B) 和P(A ^ B) ^为倒立的U
答
P(A)=13/25 P(B)=9/25 ,P(A|B)=5/9
所以P(A and B)=(9/25)*(5/9)=1/5
P(B|A)=P(A and B)/P(A)=5/13
P(A or B or both) =P(A)+P(B)-P(A and B)=13/25+9/25-1/5=18/25
P(A or B or not both) =1-P(A and B)=1-1/5=4/5
P(A'|B')= [1-P(A or B or both)]/[1-P(B)]=(7/25)/(16/25)=7/16
P(A|B')=[P(A)-P(A and B) ]/P(B')=(8/25)/(16/25)=1/2
P(A U B) 表示A,B中至少发生一个的概率
P(A ^ B) 表示A,B都发生的概率