Let events A,B,C− Tope, his brother and his sister pass an exam.
P(A)=31,P(B)=52,P(A)=83.
Events that they fail an exam are Aˉ,Bˉ,Cˉ respectively, their probabilities
P(Aˉ)=1−31=32,P(Bˉ)=1−52=53,P(Cˉ)=1−83=85.
The events Aˉ,Bˉ,Cˉ are independent,
P(Aˉ∩Bˉ∩Cˉ)=P(Aˉ)⋅P(Bˉ)⋅P(Cˉ)==32⋅53⋅85=41.
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