Question

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 at the first, second, third and fourth shots are `0.4, 0.3, 0.2` and `0.1`, respectively, What is the probability that the plane is hit when all the four shots are fired? (A) `0.4379` (B) `0.6872` (C) `0.6976` (D) `0.3507`

Answer 1

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`