# Prove or disprove conditional independence

Is the following statement true ?

"If two events E and F are independent, then they are conditionally independent given G ".

I just learned about conditional independence and need to prove or disprove it. Can someone tell me if the above statement is correct. Also can you prove or disprove it formally ?

• It's false. Suppose you are tossing a fair die. Let $E$ be the event "the die comes up even". Let $F$ be the event "the die comes up $>2$". Then let $G$ be the event "the die comes up $>1$". – lulu Apr 11 '16 at 14:26

A simple example: Consider a coin-flipping experiment, where there are two independent coin flips. Let $E, F$ be the event that head appear in the first and second flip respectively, and $G$ be the event that the total number heads equals to one.