Electronic chips Suppose the probability that a particular computer chip fails after t = a hours of operation is .

a. Find the probability that the computer chip fails after 15,000 hr of operation.

b. Of the chips that are still operating after 15,000 hr. what fraction of these will operate for at least another 15,000 hr?

c. Evaluate and interpret its meaning.

Solution:-

Step1

Given that

The probability that a particular computer chip fails after t = a hours of operation is .

Step2

To find

a. Find the probability that the computer chip fails after 15,000 hr of operation.

b. Of the chips that are still operating after 15,000 hr. what fraction of these will operate for at least another 15,000 hr?

c. Evaluate and interpret its meaning.

Step3

a. The probability that the computer chip fails after 15,000 hr of operation is

Therefore,The probability that the computer chip fails after 15,000 hr of operation is 0.75.

Step4

b. Of the chips that are still operating after 15,000 hr.The fraction of these will operate for at least another 15,000 hr is

Therefore,The fraction of these will operate for at least another 15,000 hr is 0.75

Step5

c. and interpret its meaning.

It means that all the computer chip will fail after infinity times.