SOLUTION: The "Elite Alarm Clock Radio" has a 6% defective rate (a defective alarm clock will not generate a wake up sound). After some research, you decide this is the alarm clock for you.

Question 1114954: The "Elite Alarm Clock Radio" has a 6% defective rate (a defective alarm clock will not generate a wake up sound). After some research, you decide this is the alarm clock for you. In order to insure that you wake up on time on those important mornings, you purchase three (3) Elite Alarm Clock Radios. Early tomorrow morning, you have an important job interview, so you set all three alarm clocks for the same time, knowing that you will wake up on time if at least one alarm clock works. Assume there is no power outage.
a. What is the probability (to four decimal places) that you wake up on time for your interview?
b. By how much has your probability of waking up on time improved by using three alarm clocks instead of just one?
c. What is the probability that two of the three alarm clocks work?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The "Elite Alarm Clock Radio" has a 6% defective rate (a defective alarm clock will not generate a wake up sound). After some research, you decide this is the alarm clock for you. In order to insure that you wake up on time on those important mornings, you purchase three (3) Elite Alarm Clock Radios. Early tomorrow morning, you have an important job interview, so you set all three alarm clocks for the same time, knowing that you will wake up on time if at least one alarm clock works. Assume there is no power outage.
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Binomial Problem with p(defect) = 0.06
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a. What is the probability (to four decimal places) that you wake up on time for your interview?
P(not all three fail) = 1- 0.06^3 = 1-0.000216 = 0.999784
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b. By how much has your probability of waking up on time improved by using three alarm clocks instead of just one?
P(one will not fail) = 0.94
How much more = 0.999784-0.94 = 0.059784
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c. What is the probability that two of the three alarm clocks work?
P(x = 2 when p(work)= 0.94) = 3C2*0.94^2*0.06 = binompdf(3,0.94,2) = 0.1590
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Cheers,
Stan H.
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