An anti–aircraft gun can take a maximum of 4 shots at an enemy plane moving away from it. The probabilities of hitting the plane at the first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. What is the probability that the gun hits the plane?

Question

Philoid · Accepted Answer

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