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

Two events are independent if the probability for both of them to happen equals to the product of the probability of each one separately.

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up vote 5 down vote accepted

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.

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Thank you. – user6163 Mar 29 '11 at 18:58

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