Question

A machine has fourteen identical components that function independently. It will stop working if three or more components fail. If the probability that a component fails is equal to $0.1$, find the probability that the machine will be working.

Answer 1

probability of machine not working be $p\left(e\right)$
probability of machine working be $p\left(f\right)$
wkt

$p\left(e\right)+p\left(f\right)=1$

$0.1+p\left(f\right)=1$

$p\left(f\right)=1-0.1$

$p\left(f\right)=0.9$