A manufacturing firm is producing some electronic devices with a failure rate p=
ID: 3385326 • Letter: A
Question
A manufacturing firm is producing some electronic devices with a failure rate p=1% (assume devices fail independently).
1-) The quality assurance team inspects the devices until they find a defective device.
a- What is the probability that at least one device is checked to find a defective one for the first time?
b- What is the probability that at most two devices are checked to find a defective one for the first time?
2-) What is the probability that two or more defective devices are found in a box of 10 devices?
Explanation / Answer
A manufacturing firm is producing some electronic devices with a failure rate p=1% (assume devices fail independently).
1-) The quality assurance team inspects the devices until they find a defective device.
a- What is the probability that at least one device is checked to find a defective one for the first time?
b- What is the probability that at most two devices are checked to find a defective one for the first time?
here quality team checking to find a defective (success ) one for the first time. probability function of x failures preceding the first success is q^x * p=
P(X>=1) = 1- P(X=0) = 1-0.01 = 0.99
2-) What is the probability that two or more defective devices are found in a box of 10 devices?
P(X>=2) =1-[P(X=0)+P(X=1)]=1-BINOMDIST(1,10,0.01,1)=0.0042
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