Q10. Prove that if A, B and C are independent, then AUB (A union B) is independentAdd Image/PDF files to Q10of C. Q9. If A and B are two events, prove that P(ANB) ≥ 1 − P(Ā) – P(B). [Note: Thisis a simplified version of the Bonferroni inequality.]-

In probability theory, two events are said to be independent if the occurrence of one does not…

Answered: Q10. Prove that if A, B and C are…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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For any three events A, B, & D. Such that Pr(D)>0. Prove that Pr(A U B|D) = Pr(A|D) ÷ Pr(B|D) - Pr(A n B|D)
(b) Suppose the 4-digit PINS are randomly distributed. How many peo- ple must be in a room such that the probability that two of them have the same PIN is at least 1/2? (Here "4 digits" means that the PIN cannot start with a 0.) Note: Pay special attention to the direction of the inequality in the formula(s) used for this question.
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(a) For each one of the statements below say whether the statement is true or false, explaining your answer. i. Let A and B be two events such that P(A) > 0 and P(B) > 0. If it holds that P(A|B) = 0, then P(B|A) = 1. 4 i. For two independent events A and B such that P(A) > 0) and P(B) > 0, then: P(AUB) = P(A) = P(B). iii. For a random variable X, then: Var(X)> Var(X + 2). iv. A random sample of size n is a sequence of n independent and non-identically distributed random variables. v. The standard normal distribution has fatter tails than the Student's t distribution with finite degrees of freedom. istribution with
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Q10. Prove that if A, B and C are independent, then AUB (A union B) is independent Add Image/PDF files to Q10 of C. Q9. If A and B are two events, prove that P(ANB) ≥ 1 − P(Ā) – P(B). [Note: This is a simplified version of the Bonferroni inequality.] -