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B2. (a) Starting from just the three probability axioms, prove that P(A) = 1 − P(A). (b) Let A and B be two events with P(A) = 0.8 and P(B) = 0.4. Prove the lower bound P(ANB) ≥ 0.2. You may use any of the properties of probability stated in the lecture notes. (c) Prove that the lower bound in (b) can be achieved, by giving an example of a sample space, a probability measure P and events A, BCN such that P(A) = 0.8, P(B) = 0.4 and P(ANB) = 0.2.

B2. (a) Starting from just the three probability axioms, prove that P(A) = 1 − P(A). (b) Let A and B be two events with P(A) = 0.8 and P(B) = 0.4. Prove the lower bound P(ANB) ≥ 0.2. You may use any of the properties of probability stated in the lecture notes. (c) Prove that the lower bound in (b) can be achieved, by giving an example of a sample space, a probability measure P and events A, BCN such that P(A) = 0.8, P(B) = 0.4 and P(ANB) = 0.2.

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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B2. (a) Starting from just the three probability axioms, prove that P(A) = 1 − P(A). (b) Let A and B be two events with P(A) = 0.8 and P(B) = 0.4. Prove the lower bound P(ANB) ≥ 0.2. You may use any of the properties of probability stated in the lecture notes. (c) Prove that the lower bound in (b) can be achieved, by giving an example of a sample space, a probability measure P and events A, BCN such that P(A) = 0.8, P(B) = 0.4 and P(ANB) = 0.2.
Transcribed Image Text:B2. (a) Starting from just the three probability axioms, prove that P(A) = 1 − P(A). (b) Let A and B be two events with P(A) = 0.8 and P(B) = 0.4. Prove the lower bound P(ANB) ≥ 0.2. You may use any of the properties of probability stated in the lecture notes. (c) Prove that the lower bound in (b) can be achieved, by giving an example of a sample space, a probability measure P and events A, BCN such that P(A) = 0.8, P(B) = 0.4 and P(ANB) = 0.2.
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