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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.

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
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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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