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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
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In Example 1.4-5, suppose that the probability of failure

Chapter 1, Problem 14E

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QUESTION:

In Example 1.4-5, suppose that the probability of failure of a component is \(p=0.4\). Find the probability that the system does not fail if the number of redundant components is

(a) \(3\).

(b) \(8\).

Equation Transcription:

Text Transcription:

p=0.4  

3  

8

Questions & Answers

QUESTION:

In Example 1.4-5, suppose that the probability of failure of a component is \(p=0.4\). Find the probability that the system does not fail if the number of redundant components is

(a) \(3\).

(b) \(8\).

Equation Transcription:

Text Transcription:

p=0.4  

3  

8

ANSWER:

Answer :

Step 1 of 2 :

Probability of failure of component is p=0.4

Let number of redundant is n.

P(system does not fail) =

P(system does not fail) =

P(system does not fail) =

a).

Now we have to find the probability that the system does not fails.

If the number of redundant is 3.

P(system does not fail) =

Here n=3 and p=0.40

Substitute n and p values.

P(system does not fail) =

P(system does not fail) =

P(system does not fail) =

Therefore the probability that the system does not fails is 0.936

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