Question

A radar complex consists of eight units that operate independently. The probability that a unit detects an incoming missile is $0.9$. Find the probability that an incoming missile will
not be detected by any unit.

Answer 1

Probability of not detecting missile $=0.1$

As all units are dependent

$\Rightarrow P(A_1\cap A_2\cap ....\cap A_8)={\pi }_{i=1}^{8}P\left(A_i\right)$

$=(0.1{)}^8={10}^{-8}$