Question

A phone component has to go through twenty different check ups. The component will have to be re-engineered again if it fails any one of these checkups. Supposes the probability of the component failing a checkup is the same for all checkups and the results of the checkup are independent of each other. If 15% of components need to be re-engineered, what is the probability that the component fails a checkup?

Answer 1

Let p = probability that the component not fails to checkup

It is given that the component will have to be reengineered again if it fails any one of these checkup.

Also the probability of the components need to be reengineered is given as 0.15

So here we need to find p such that

the component fails a checkup = 1 - P ( all checkup are good) =1 - (p)²⁰ = 0.15

p^{​​​​​​20}​ = 0.85

So p = 0.9919

So 1- p = probability that the component fails to checkup = 1 - 0.9919 = 0.0081. This is the final answer.