An anti-aircraft gun can take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane in the first second third, and fourth shot are respectively 0.2, 0.4 0.2 and 0.1. Find the probability that the gun hits the plane.

Explanation

Let `P(H_(1))=0.4,P(H_(2))=0.3,P(H_(3))=0.2,P(H_(4))=0.1`
P(gun hits the plane)
`=1-P("gun does not his the plane")`
`=1-P(bar(H)_(1)).P(bar(H)_(2)).P(bar(H)_(3)).P(bar(H)_(4))`
`=1-(0.6)(0.7)(0.8)(0.9)=1-0.3024=0.6976`