# Solved: An electronic device is made up of two components A and B such that the device would work satisfactorily as long as at least one of the components works

#### ByDr. Raju Chaudhari

Feb 26, 2021

An electronic device is made up of two components A and B such that the device would work satisfactorily as long as at least one of the components works. The probability of failure of component A is 0.02 and that of B is 0.1 in some fixed period of time. If the components work independently, find the probability that the device will work satisfactorily during the period.

#### Solution

Let $A$ be the event that component A work. Let $B$ be the event that component B work.

The probability of failure of component A is 0.02, i.e., $P(A^\prime) = 0.02$ and the probability of failure of component B is 0.1, i.e., $P(B^\prime) = 0.1$.

Then $P(A)= 1-P(A^\prime) = 0.98$ and, $P(B) = 1- P(B^\prime)=0.9$.

The probability that the device will work satisfactorily during the period is given by $P(A\cap B)$.

As process of occurrence of both the event is independent to each other, we use

$P(A\cap B) = P(A)*P(B)$

The probability that the device will work satisfactorily during the period is $P(A\cap B)$.

That is, $P(A\cap B) = 0.98*0.9 = 0.882$.