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The inclusion-exclusion principle shows that for two events $P[A \cup B]=P[A]+P-P[A \cap B]$ and for three events $P[A \cup B \cup C] = P[A] + P + P[C] - P[A \cap B] - P[A \cap C] - P[B \cap C] + P[A \cap B \cap C]$.
Using these as a guideline what is $P[A \cup B \cup C \cup D]$? In general, how many terms will be in $$P\left[ \bigcup_{i=1}^{n} A_i \right]$$?
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Using these as a guideline what is $P[A \cup B \cup C \cup D]$? In general, how many terms will be in $$P\left[ \bigcup_{i=1}^{n} A_i \right]$$?
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