Question

Which expression gives the probability of three events occurring together?

Options

• \[P(E \cap F \cap G)=P(E)\cdot P(F\mid E)\cdot P(G\mid E\cap F)\]

• \[P(E \cap F \cap G)=P(E\mid F)\cdot P(F\mid G)\]

• \[P(E \cap F \cap G)=P(E)+P(F)+P(G)\]

• \[P(E \cap F \cap G)=P(E)\cdot P(F)\cdot P(G)\]

Answer 1

For three events, first use \[P(E)\], then \[P(F\mid E)\], and finally \[P(G\mid E\cap F)\]. The last factor conditions on both preceding events.