2. Suppose = {a, b, c, d} and that {a} is an event. (a) What sets must be in F? That is, what other subsets of must be events? (Do not put all subsets of 2 in F unless they all must be there.) (b) Suppose P({a}) = 1/4. What other events can you compute the proba- bility of?

2. Suppose = {a, b, c, d} and that {a} is an event. (a) What sets must be in F? That is, what other subsets of must be events? (Do not put all subsets of 2 in F unless they all must be there.) (b) Suppose P({a}) = 1/4. What other events can you compute the proba- bility of?

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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Question

2. Suppose = {a, b, c, d} and that {a} is an event.
(a) What sets must be in F? That is, what other subsets of 2 must be
events? (Do not put all subsets of 2 in F unless they all must be there.)
(b) Suppose P({a}) = 1/4. What other events can you compute the proba-
bility of?

Expert Solution

Step 1

Given that $Ω = {a, b, c, d}$ and that ${a}$ is an event.

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6. Establish what is meant by (a) a pair of mutually exclusive events and (b) a pair of statistically independent events. Prove, with reference to the axioms of probability and the rules of boolean algebra, that P(AUB) = P(A) + P(B) – P(AN B). The probability that a smoker who consumes over 40 cigarettes a day will suffer from chronic respiratory illness is 0.4. The probability that he will suffer from heart disease is 0.5. The probability that he will suffer from at least one of these ailments is 0.6 (i) Find the probability that the smoker will suffer from both ailments, (ii) Find the probability that he will suffer from heart disease given that he suffers from chronic respiratory illness.
13.
Example 3-28. Let P (A) = p, P (A \B) = q, P (B | A) = r. Find relations betwe number p, q, r for the following cases : (a) Events A and B are mutually exclusive. (b) A and B are mutually exclusive and collectively exhaustive. (c) A is sub-event of B ; B is a sub-event of A. (d) Ā andB are mutually exclusive.
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