# The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a​ student's alarm clock has a 19.1​% daily failure rate. If the student has two such alarm​ clocks, what is the probability that they both fail on the morning of an important final​ exam?

Question

The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a​ student's alarm clock has a 19.1​% daily failure rate. If the student has two such alarm​ clocks, what is the probability that they both fail on the morning of an important final​ exam?

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Step 1

Given:

Probability that alarrm clock fails a day = 0.191,

We have two such clocks and we have to find the probability that both clock fails on a exam day.

Step 2

We have two clocks and they both are independent of each other So, to get the answer of this question we will use independent event probability concept.

Independet Event Proability : It refers to the probability of occurance of  one event will not affect the probability of other.

#. The probability of intersection between two event is equal to the multiplication of probabilities of these two events.

#Note: Intersection Sign defines the common part between two events .

Since here both clocks fails so we are using intersection.

Step 3

A = Alarm clock no. 1 fails

B = Alarm clock  no. 2 fails

Probabili...

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