Independence of more than two events 10/20

I gave an example in class of three events E,F and G, such that E and F are independent and E and G are independent , but $F\cap G$ and E are NOT independent.

In general for 3 events, we say the three events are mutually independent iff all couples of events are independent 2 by 2 and

$$P(E\cap F \cap G)=P(E)\times P(F) \times P(G)$$

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