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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

Reliability of a Machine A machine that is used in a manufacturing process has four separate components, each of which has a 0.01 probability of failing on any given day. If any component fails, the entire machine breaks down. Find the probability that on a given day the indicated event occurs.

(a) The machine breaks down.

(b) The machine does not break down.

(c) Only one component does not fail.

To determine

(a)

To find:

The probability that on a given day machine breaks down.

Explanation

Given:

The number of components is 4.

The probability of a component failing on any given day is 0.01.

Approach:

Write the expression for the probability of success in a trial.

P(S)=p

Here, P(S) is the probability of success.

Write the expression to find the probability of failure in a trial.

P(F)=1pq=1p ……(1)

Here, q=P(F) is probability of failure.

Write the expression to find the probability of getting exactly r success in given number of independent trials of the experiment.

P(rsuccessesinntrials)=C(n,r)prqnr …... (2)

Here, n is the number of trial and r is the number of success in the given experiment.

Write the formula to find the number of combinations.

C(n,r)=n!r!(nr)!

Substitute n!r!(nr)! for C(n,r) in equation (2). Then,

P(rsuccessesinntrials)=(n!r!(nr)!)prqnr ……(3)

To determine

(b)

To find:

The probability that on a given day machine does not break down.

To determine

(c)

To find:

The probability that on a given day only one component does not fail.

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Chapter 14 Solutions

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