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Get Full Access to Applied Statistics And Probability For Engineers - 6 Edition - Chapter 2.6 - Problem 157e
Get Full Access to Applied Statistics And Probability For Engineers - 6 Edition - Chapter 2.6 - Problem 157e

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# Solved: The following circuit operates if and only if ISBN: 9781118539712 55

## Solution for problem 157E Chapter 2.6

Applied Statistics and Probability for Engineers | 6th Edition

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Problem 157E

Problem 157E

The following circuit operates if and only if there is a path of functional devices from left to right. The probability that each device functions is as shown. Assume that the probability that a device is functional does not depend on whether or not other devices are functional. What is the probability that the circuit operates? Step-by-Step Solution:

Solution :

Step 1 of 1:

Given if and only if circuit a path of functional device from left to right.

Then the diagram is given below. Our goal is:

We need to find the probability that the circuit operates.

Now we have to find the probability that the circuit operates.

From the above circuit we have to calculate P( ), P( ), P( ), P( ) , P( ), and P( ).

P(A) = P( )+P( )-P ( )

P(A) = P( )+P( )-P( ) P( )

P(A) = 0.9+0.95-(0.9 0.95)

P(A) = 1.85-0.855

P(A) = 0.995

Therefore, P(A)=0.995.

P(B) = P( )+P( )-P ( )

P(B) = P( )+P( )-P( ) P( )

P(B) = 0.9+0.95-(0.9 0.95)

P(B) = 1.85-0.855

P(B) = 0.995

Therefore, P(B)=0.995.

P(C) = P( )+P( )-P ( )

P(C) = P( )+P( )-P( ) P( )

P(C) = 0.8+0.9-(0.8 0.9)

P(C) = 0.98

Therefore, P(C)=0.98.

The probability that the circuit operates is

P(A) P(B) P(C) = 0.995 0.995 0.98

P(A) P(B) P(C) = 0.9702

Therefore, the probability that the circuit operates is 0.9702.

Step 2 of 1

##### ISBN: 9781118539712

Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9781118539712. This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers , edition: 6. Since the solution to 157E from 2.6 chapter was answered, more than 881 students have viewed the full step-by-step answer. The answer to “The following circuit operates if and only if there is a path of functional devices from left to right. The probability that each device functions is as shown. Assume that the probability that a device is functional does not depend on whether or not other devices are functional. What is the probability that the circuit operates?” is broken down into a number of easy to follow steps, and 56 words. This full solution covers the following key subjects: functional, Probability, device, operates, Devices. This expansive textbook survival guide covers 97 chapters, and 2005 solutions. The full step-by-step solution to problem: 157E from chapter: 2.6 was answered by , our top Statistics solution expert on 07/28/17, 07:57AM.

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