Question

If three events of a sample space are $E$, $F$ and $G$, then $P(E\, \cap\, F \cap\, G)$ is equal to

• A. $P(E)P(F|E)P(G|(E\cap F))$
• B. $P(E) \,P(F|E)\, P(G |EF ))$
• C. Both $(a)$ and $(b)$
• D. None of these

Answer 1

Answer: (C)

Both $(a)$ and $(b)$

Answer 2

If $E$, $F$ and $G$ are the three events of sample space, then we have $P(E\, \cap\, F \cap\, G) = P(E)\, P(F|E)\, P(G|(E\cap F))$ $= P(E)\, P(F|E)\, P(G|EF)$