Given that an anti–aircraft gun can take a maximum of 4 shots at an enemy plane moving away from it.
Let
A = hitting the plane at first shot P(A) = 0.4
B = hitting the plane at second shot
P(B) = 0.3
C = hitting the plane at third shot
P(C) = 0.2
D = hitting the plane at fourth shot
P(D) = 0.1 P
(gun hits the plane) = 1 – P(gun does not hit the plane)
= 1 – P(none of the four shots hit the plane)
=1 – [(1 – 0.4)(1 – 0.3)(1 – 0.2)(1 – 0.1)]
=1 – (0.6)(0.7)(0.8)(0.9)
=1 – 0.3024 = 0.6976