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Given that I have a fair coin which I toss three times, how do I:

a) Find three events $A$ , $B$, and $C$ such that no two are independent but $P( A \cap B \cap C) = P( A ) P( B) P( C)$ ?

b) Find three events $A$ , $B$, and $C$ such that every two are independent but all three are not independent: $P( A \cap B \cap C) \not= P( A ) P( B) P( C)$ ?

How would I approach a problem like this ? I started by drawing a binary tree that ended up with 8 leaves but I have no idea how to use it to get the answers. Any help would be appreciated.

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  • $\begingroup$ is that homework? $\endgroup$
    – Antoine
    Commented Sep 6, 2015 at 16:33
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    $\begingroup$ Please add the [self-study] tag & read its wiki. Then tell us what you understand thus far, what you've tried & where you're stuck. We'll provide hints to help you get unstuck. $\endgroup$
    – gung - Reinstate Monica
    Commented Sep 6, 2015 at 17:39

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