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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).

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.CR: Chapter 12 Review
Problem 11CR
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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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