The principle of redundaney isused when System reliabilty s improved through rad

Question

The principle of redundaney isused when System reliabilty s improved through radundanrt or backup components. Assume that a Students alarm clock has a 70 % daily failure rate. Complete parts Ca) through (d) below. a.) what is the probabifrty that the students alarm Clook will not work on the mornirg of an important final exam? Croundkdecimal places as needed) (b) IF the student has tuwo Such alarm clocks, what is the probabiliy that thuy both fal on the morning of an important-final exam?Round to 5 decimal Cc.) What is tha probability of not being awakened if the. student uses three independent alarm docks? paces as nuaded) CRound to 5 decimal placas as nda) a Do the Setond and thid alarm docks resut+n greaty improved reliability? Cd.)

Explanation / Answer

a)
probability that alarm clock will not work = 0.076

b)
Probability that both alarm clock fails = 0.076 * 0.076 = 0.00578

c)
If three alarm clocks are used and all failed, probability = 0.076 * 0.076 * 0.076 = 0.00044

d)
Yes, second and third alarm clock improves the reliability

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