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Statistics / Probability and Statistical Inference 9 / Chapter 1.1 / Problem 1.1-9

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

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Roll a fair six-sided die three times. Let A1 = {1 or 2 on the first roll}, A2 = {3 or 4

Chapter 1, Problem 1.1-9

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QUESTION:

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.

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QUESTION:

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.

ANSWER:

Step 1 of 3

Given:

A six-sided fair die is rolled six times.

The provided probabilities are,

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