Question

Which conditions are required for \[P(E \cap F \cap G)=P(E)\cdot P(F\mid E)\cdot P(G\mid E\cap F)\]?

Options

• \[P(E)\ne0\] and \[P(E\cap F)\ne0\]

• \[P(F)\ne0\] and \[P(G)\ne0\]

• \[P(E)=P(F)=P(G)\]

• \[P(E)=0\] and \[P(E\cap F)=0\]

Answer 1

The conditional probabilities \[P(F\mid E)\] and \[P(G\mid E\cap F)\] require nonzero conditioning probabilities. Therefore, \[P(E)\ne0\] and \[P(E\cap F)\ne0\].