A manufacturing firm is producing some electronic devices wi

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?

Solution

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