the principle of redundancy is used when system reliability is improved through redundant or backup…

the principle of redundancy is used when system reliability is improved through redundant or backup components. assume that a students alarm clock has a 18.1% daily failure rate. complete parts (a) through (d) below. a. what is the probability that the students alarm clock will not work on the morning of an important final exam? 0.181 (round to three decimal places as needed.) b. if the student has two such alarm clocks, what is the probability that they both fail on the morning of an important final exam? (round to five decimal places as needed.)

the principle of redundancy is used when system reliability is improved through redundant or backup components. assume that a students alarm clock has a 18.1% daily failure rate. complete parts (a) through (d) below. a. what is the probability that the students alarm clock will not work on the morning of an important final exam? 0.181 (round to three decimal places as needed.) b. if the student has two such alarm clocks, what is the probability that they both fail on the morning of an important final exam? (round to five decimal places as needed.)

Answer

Explanation:

Step1: Identify failure - rate of one clock

The failure rate of one alarm clock is given as $p = 0.181$.

Step2: Use multiplication rule for independent events

Since the two alarm - clocks are independent, the probability that both fail is the product of their individual failure probabilities. Let $P(A)$ and $P(B)$ be the failure probabilities of the first and second alarm - clocks respectively. For independent events $A$ and $B$, $P(A\cap B)=P(A)\times P(B)$. Here, $P(A) = P(B)=0.181$. So, $P(A\cap B)=0.181\times0.181$.

Step3: Calculate the result

$0.181\times0.181 = 0.032761\approx0.03276$

Answer:

$0.03276$