# probability - Independence

I'm trying to find an example for n events that each k (k < n) are independent, but the n events together are dependent.

Two events are independent if the probabaility for both of them to happen equales to the product of the probablity of each one separately.

Thank you.

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Suppose you toss a coin $n-1$ times. For $i$ from $1$ to $n-1$, let $A_i$ be the event that the $i$th toss comes up heads. Let $A_n$ be the event that the total number of tosses that came up heads is even. Then $\{ A_1, A_2, \ldots, A_n \}$ is dependent but every proper subset is independent.