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Suppose that A, B, and C are mutually independent events

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

Solution for problem 9E Chapter 1.4

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

Suppose that A, B, and C are mutually independent events and that P(A) = 0.5, P(B) = 0.8, and P(C) = 0.9. Find the probabilities that (a) all three events occur, (b) exactly two of the three events occur, and (c) none of the events occurs.

Step-by-Step Solution:

Step 1 of 5:

Given that events A,B and C are mutually independent.

Also it is given that P(A)=0.5,P(B)=0.8 and P(C)=0.9.

Step 2 of 5:

(a)

Here we have to find the probability that all the three events occur.

Probability that all the three events occur is the probability of the event ABC.

Since the events are mutually independent, the probability of ABC is given by

P(ABC)=P(A)*P(B)*P(C)

                    =(0.5)*(0.8)*(0.9)

                   =0.36

Therefore, probability of all the three events occur is 0.36.

Step 3 of 5:

(b)

Here we have to find the probability that exactly two of the events occur.

Probability that exactly two of the three events occur is given by,

P(AB)+P(AC)+P(BC)

where, ,, denotes the non occurrence of the events A,B and C respectively.

We know that P(A)+P()=1.

Therefore,

P()=1-P(A)

         =1-0.5

         =0.5

P()=1-P(B)

         =1-0.8

         =0.2

and

P()=1-P(C)

          =1-0.9

           =0.1

Step 4 of 5

Chapter 1.4, Problem 9E is Solved
Step 5 of 5

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

This full solution covers the following key subjects: Events, occur, none, independent, mutually. This expansive textbook survival guide covers 59 chapters, and 1476 solutions. The answer to “Suppose that A, B, and C are mutually independent events and that P(A) = 0.5, P(B) = 0.8, and P(C) = 0.9. Find the probabilities that (a) all three events occur, (b) exactly two of the three events occur, and (c) none of the events occurs.” is broken down into a number of easy to follow steps, and 46 words. 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. Since the solution to 9E from 1.4 chapter was answered, more than 253 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 9E from chapter: 1.4 was answered by , our top Statistics solution expert on 07/05/17, 04:50AM.

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