Question

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/

Answer 1

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