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

Options

A. `((9)/(10))^(4)`
B. `9((1)/(10))^(5)`
C. `(1)/(10^(8))`
D. `(1)/(10)`

Answer

C

Explanation

(c ) Given, probability that a unit detects an incoming missile,
`p=0.9=(9)/(10)`
`=1-p=1-(9)/(10)=(1)/(10)` and n=8
`:.` Required probability `=""^(8)C_(0)((9)/(10))^(0)((1)/(10))^(8)=(1)/(10^(8))`