Question

A circuit contains five components and will fail if two out of the five components fail. If the failure of each component is random and the probability of failure of each component is the same, then what is the maximum failure rate for each component if the failure rate of the overall circuit is to be less than 10%

Answer 1

Explanation:

Given that a circuit contains five components and will fail if two out of the five components fail.

Let X be the no of components that fail. Then x can take values as 0,1,2,3,4 or 5

If the failure of each component is random and the probability of failure of each component is the same then X is binomial with (5,p)

`P(X<2)` is the failure rate of overall circuit

This is less than 10% = 0.1

i.e. This will be equal to

`P(0)+P(1)\\=(1-p)^5 +5(p)(1-p)^4` <0.10

Solving we get p =0.58

i.e. maximum failure rate can be 0.58