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C1. Let 2 be a sample space with a probability measure P, and let A, B C be events. For each of the ollowing statements, state whether the statement is true or false (that is, always true or sometimes False). If it is true, briefly justify the statement; if it is false, give a counterexample. (a) If P(A) ≤ P(B), then A C B. (b) P(An B) + P(An Bc) = P(A). (c) P(AUB) ≤ P(A) (d) If A and B are disjoint, then P((AUB)) = 1 - P(A) – P(B).

C1. Let 2 be a sample space with a probability measure P, and let A, B C be events. For each of the ollowing statements, state whether the statement is true or false (that is, always true or sometimes False). If it is true, briefly justify the statement; if it is false, give a counterexample. (a) If P(A) ≤ P(B), then A C B. (b) P(An B) + P(An Bc) = P(A). (c) P(AUB) ≤ P(A) (d) If A and B are disjoint, then P((AUB)) = 1 - P(A) – P(B).

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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C1. Let 2 be a sample space with a probability measure P, and let A, B C be events. For each of the following statements, state whether the statement is true or false (that is, always true or sometimes false). If it is true, briefly justify the statement; if it is false, give a counterexample. (a) If P(A) ≤ P(B), then A C B. (b) P(An B) + P(An Bc) = P(A). (c) P(AUB) ≤ P(A) A (d) If A and B are disjoint, then P((AUB)) = 1 - P(A) - P(B).
Transcribed Image Text:C1. Let 2 be a sample space with a probability measure P, and let A, B C be events. For each of the following statements, state whether the statement is true or false (that is, always true or sometimes false). If it is true, briefly justify the statement; if it is false, give a counterexample. (a) If P(A) ≤ P(B), then A C B. (b) P(An B) + P(An Bc) = P(A). (c) P(AUB) ≤ P(A) A (d) If A and B are disjoint, then P((AUB)) = 1 - P(A) - P(B).
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