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Question: Show that if E₁, E₂, E₃ are independent, then E₁ is independent from E₂∪E₃. (Hint. By the Distributive Law, P(E₁ ∩ (E₂ ∪ E₃)) = P((E₁ ∩ E₂) ∪ (E₁∩ E₃)). Using the formula for the probability of the union of two events (part (1) of Proposition 2.4-2) and the independence of E₁, E₂, E₃, write this as P(E₁)P(E₂) + P(E₁)P(E₃) - P(E₁)P(E₂∩ E₃) and finish the proof.)

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