# Question: Duplicate the method of proof used in Exercise 2 12 to

Duplicate the method of proof used in Exercise 2.12 to show that

P(A ∪ B ∪ C ∪ D) = P(A) + P(B) + P(C) + P(D)

- P(A ∩ B) - P(A ∩ C) - P(A ∩ D)

- P(B ∩ C) - P(B ∩ D) - P(C ∩ D)

+ P(A ∩ B ∩ C) + P(A ∩ B ∩ D)

+ P(A ∩ C ∩ D) + P(B ∩ C ∩ D)

- P(A ∩ B ∩ C ∩ D)

P(A ∪ B ∪ C ∪ D) = P(A) + P(B) + P(C) + P(D)

- P(A ∩ B) - P(A ∩ C) - P(A ∩ D)

- P(B ∩ C) - P(B ∩ D) - P(C ∩ D)

+ P(A ∩ B ∩ C) + P(A ∩ B ∩ D)

+ P(A ∩ C ∩ D) + P(B ∩ C ∩ D)

- P(A ∩ B ∩ C ∩ D)

## Answer to relevant Questions

Prove by induction that For Any finite sequence of events E1, E2, ∪ . ., And En. Duplicating the method of proof of Theorem 2.10, show that P(A ∩ B ∩ C ∪ D) = P(A) · P(B| A) · P(C| A ∩ B) · P(D| A ∩ B ∩ C) provided that P(A ∩ B ∩ C) ≠ 0. If A1, A2,…, An are independent events, prove that P(A1 ∪ A2,···, An) = 1-{1- P(A1) } · {1- P(A2) } … {1- P(A ∩) } Among the eight cars that a dealer has in his show-room, Car 1 is new And has air- conditioning, power steering, And bucket seats; Car 2 is one year old And has air-conditioning, but neither power steering nor bucket seats; ...In Figure 2.14, E, T, And N are the events that a car brought to a garage needs an engine overhaul, trans-mission repairs, or new tires. Express in words the events represented by (a) Region 1; (b) Region 3; (c) Region 7; ...Post your question