(a) The inclusion-exclusion formula for A1, A2, and A3 is:P(A1... | Filo

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Prove that for any events A1, A2, A3, ..., An we have the inclusion-exclusion formula:P(A1 U A2 U A3 U ... U An) = P(A1) P(A2) P(A3) ... P(An) - P(A1 ∩ A2) - P(A1 ∩ A3) - ... - P(A1 ∩ An) - P(A2 ∩ A3) - ... - P(A2 ∩ An) - ... - P(A(n-1) ∩ An) P(A1 ∩ A2 ∩ A3) P(A1 ∩ A2 ∩ A4) ... (-1)^(n-1) * P(A1 ∩ A2 ∩ ... ∩ An)

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