An electronic office product contains 5000 electronic components. Assume that the probability that each component operates without failure during the useful life of the product is 0.999, and assume that the components fail independently. Approximate the probability that 10 or more of the original 5000 components fail during the useful life of the product.

Solution 101E

Step1 of 2:

Let us consider a random variable X it presents the lifetime of a product. We have An electronic office product contains 5000 electronic components.

We need to find the probability that 10 or more of the original 5000 components fail during the useful life of the product.

Step2 of 2:

Let q = The probability that the component does not fail

q = 0.999,

Then, p = 1 - q

= 1 - 0.999

= 0.001.

Now, the probability that 10 or more fail is:

Where, is obtained from Excel by using the function “=binomdist(X,n,p,false).”

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