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P(A1)=0.1,P(A2)=0.5,P(B|A1)=0.2,P(B|A2)=0.6,P(B|A3)=0.1.求P(A1|B)

题目详情
P(A1)=0.1,P(A2)=0.5,P(B|A1)=0.2,P(B|A2)=0.6,P(B|A3)=0.1.求P(A1|B)
▼优质解答
答案和解析
P(B|A1)=P(A1B)/P(A1)=0.2,
P(A1B)=0.02
P(B|A2)=P(A2B)/P(A2)=0.6,
P(A2B)=0.3
P(B|A3)=P(A3B)/P(A3)=0.1
P(A3)=?差条件=1-P(A1)-P(A2)=0.4
P(A3B)=0.04
P(B)=P(A1B)+P(A2B)+P(A3B)=0.36
P(A1|B)=P(A1B)/P(B)=0.02/0.36=1/18