Let A₁, A2, and A3 be independent. Show that A₁, A2, and Ag are independent. You may freely use the result, from recitation, that the complements of two independent events are independent. Suppose that A₁ is independent of A3 and also that A₂ is independent of A3. Is it true that A₁ U A2 is independent of A3? Prove or give a counterexample.

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A: Solution:  Given information:  P(K)= 0.7  P(L)= 0.3 P(K∩L)= 0.21

Q: Let A, B and D be events. Show that p(A ∪ B|D) = P(A|D) + P(B|D) − ?(A ∩ B|D).

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Q: Let A and B be events. Point (prove) that:   a. P(A \ B) = P(A) − P(A ∩ B).    b) If 0 < P(B) < ,…

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Q: Use Bayes' theorem to solve this problem. A storeowner purchases stereos from two companies. From…

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Q: Theorem 3-9. If A, B, C are mutually independent events then A UB and C are also ndependent.

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Q: Theorem 3.10. If the events A and B are such that P(A) #0, P(B) ±0 and A is independent of B, then B…

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Q: : If A, B, C are mutually independent events then A UB and C are also independent.

A: Answer: For the given data,

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Q: Suppose that vehicles taking a particular freeway exit can turn right (R), or turn left.(L).…

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Q: 1. Two events are independent if

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

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Q: Calculate P (A ∩ B) Are events A AND B independent?

A: