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Let A and B be events having positive probability. State

A First Course in Probability | 9th Edition | ISBN: 9780321794772 | Authors: Sheldon Ross ISBN: 9780321794772 63

Solution for problem 23STE Chapter 3

A First Course in Probability | 9th Edition

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A First Course in Probability | 9th Edition | ISBN: 9780321794772 | Authors: Sheldon Ross

A First Course in Probability | 9th Edition

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Problem 23STE

Problem 23STE

Let A and B be events having positive probability. State whether each of the following statements is (i) necessarily true, (ii) necessarily false, or (iii) possibly true.

(a) If A and B are mutually exclusive, then they are independent.

(b) If A and B are independent, then they are mutually exclusive.

(c) P(A) = F(B) = .6, and A and B are mutually exclusive.

(d) P(A) = P(B) = .6, and A and B are independent.

Step-by-Step Solution:

Solution:

Step 1 of 5:

Let A and B are events with positive probability.

We have to find the given statements are (i) necessarily true, (ii) necessarily false, or (iii) possibly true.

  1. If A and B are mutually exclusive, then they are independent.
  2. If A and B are independent, then they are mutually exclusive.
  3. P(A), PB) = 0.6, then A and B are mutually exclusive.
  4. P(A), P(B) = 0.6, and A and B are independent.

Step 2 of 5

Chapter 3, Problem 23STE is Solved
Step 3 of 5

Textbook: A First Course in Probability
Edition: 9
Author: Sheldon Ross
ISBN: 9780321794772

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Let A and B be events having positive probability. State