An anticraft gun can take a maximum of four shots at an enemy plane moving away from it. The probabilities of hitting the plane at the first, second, third and the fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. What is the probability that the gun hits the plane. Choices.
A) 0.3024  B) 0.6976  C) 0.44  D) 0.868  E) 0.839
Explanation :   Let E ≡ the gun hits the plane i.e at least one of the 4 shots hits the plane.   P(E) = 1 - P( none hits the plane)   = 1 - P( ~S1 ~S2 ~S3 ~S4).   ( S1 S2 S3 S4 are the probabilities of shots)   = 1 - P( ~S1) x P(~S2) x P(~S3) x P(~S4).   = 1 - (1-0.4)(1-0.3)(1-0.2)(1-0.1)   =1 - [0.6 x 0.7 x 0.8 x 0.9 ]   = 1 - 0.3024.   = 0.6976.   Hence, the required probabilities is 0.6976.   Answer : 0.6976
<result>B</result>
An anticraft gun can take a maximum of four shots at an enemy plane moving away from it. The probabilities of hitting the plane at the first, second, third and the fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. What is the probability that the gun hits the plane.