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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 $P( A U B U C) = P( A ) P( B) P( C)$ ?

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

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.

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.