Show that if e1 e2 e3 are independent then e1 is


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) ∪ (E∩ 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(E∩ E3) and finish the proof.)

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Basic Statistics: Show that if e1 e2 e3 are independent then e1 is
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