Problem 2 1. For any three events A, B, C, with all P(A), P(B), P(C), and P(An B) > 0. Prove that P(An BnC)=P(A)P(B|A)P(C|An B). 2. Suppose that A and B are events such that P(A/B) = P(B|A). For P(AUB) P(An B) > 0, prove that P(B) > . 3. For any event E, either prove P(E|E) = 1, or provide a counterexample. = and
Problem 2 1. For any three events A, B, C, with all P(A), P(B), P(C), and P(An B) > 0. Prove that P(An BnC)=P(A)P(B|A)P(C|An B). 2. Suppose that A and B are events such that P(A/B) = P(B|A). For P(AUB) P(An B) > 0, prove that P(B) > . 3. For any event E, either prove P(E|E) = 1, or provide a counterexample. = and
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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Solve all parts of problem 2 plz
Transcribed Image Text:Problem 2
1. For any three events A, B, C, with all P(A), P(B), P(C), and P(An B) > 0. Prove that
P(An BnC) = P(A)P(B|A)P(C|An B).
2. Suppose that A and B are events such that P(A|B)
P(An B) > 0, prove that P(B) > .
3. For any event E, either prove P(EE) = 1, or provide a counterexample.
=
P(B|A). For P(AUB) = 1 and
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