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Roll a fair six-sided die three times. Let A1 ={1 or 2 on

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman ISBN: 9780321923271 41

Solution for problem 9E Chapter 1.1

Probability and Statistical Inference | 9th Edition

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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Probability and Statistical Inference | 9th Edition

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Problem 9E

PROBLEM 9E

Roll a fair six-sided die three times. Let A1 ={1 or 2 on the first roll}, A2 = {3 or 4 on the second roll}, and A3 = {5 or 6 on the third roll}. It is given that P(Ai) = 1/3, i = 1, 2, 3; P(Ai Aj) = (1/3)2, I ≠ j; and P(A1 ∩ A2 ∩ A3) = (1/3)3.

(a) Use Theorem 1.1-6 to find P(A1 ∪ A2 ∪ A3).

(b) Show that P(A1 ∪ A2 ∪ A3) = 1 − (1 − 1/3)3.

Step-by-Step Solution:

Answer :

Step 1 of 3 :

Given, Roll a fair six- sided die three times.

Let =

       =  and

       =

We have, P() = ⅓ , i = 1, 2, 3.

                P() = (, where, I j   and

               P() = (.

Step 2 of 3

Chapter 1.1, Problem 9E is Solved
Step 3 of 3

Textbook: Probability and Statistical Inference
Edition: 9
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
ISBN: 9780321923271

Since the solution to 9E from 1.1 chapter was answered, more than 960 students have viewed the full step-by-step answer. The answer to “Roll a fair six-sided die three times. Let A1 ={1 or 2 on the first roll}, A2 = {3 or 4 on the second roll}, and A3 = {5 or 6 on the third roll}. It is given that P(Ai) = 1/3, i = 1, 2, 3; P(Ai ? Aj) = (1/3)2, I ? j; and P(A1 ? A2 ? A3) = (1/3)3.(a) Use Theorem 1.1-6 to find P(A1 ? A2 ? A3).(b) Show that P(A1 ? A2 ? A3) = 1 ? (1 ? 1/3)3.” is broken down into a number of easy to follow steps, and 86 words. The full step-by-step solution to problem: 9E from chapter: 1.1 was answered by , our top Statistics solution expert on 07/05/17, 04:50AM. Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271. This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9. This full solution covers the following key subjects: Roll, die, Find, given, let. This expansive textbook survival guide covers 59 chapters, and 1476 solutions.

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Roll a fair six-sided die three times. Let A1 ={1 or 2 on