An anti-aircraft gun can take a maximum of four shots at an enemy plane moving away from it. The pro

Question

An anti-aircraft gun can take a maximum of four shots at an enemy plane moving away from it. The probabilities of hitting the plane at the $1^{	ext {st }}, 2^{	ext {nd }}, 3^{	ext {rd }}$, and $4^{	ext {th }}$ shots are 0.4 , $0.3,0.2$ and 0.1 respectively. What is the % probability that the gun hits the plane (Round off to nearest integer)?

Professor PC Thomas Classes · Answer

Let $A, B, C, D$ be the events that the gun hits the target $1^{	ext {st }}, 2^{	ext {nd }}, 3^{	ext {rd }}$ and $4^{	ext {th }}$ respectively.\ Given $P(A)=0.4, P(B)=0.3, P(C)$\ $=0.2, P(D)=0.1$\ Probability that the gun hits the target $=1-$ Probability that the gun does not hit the enemy's plane\ $=1-P(\bar{A}) P(\bar{B}) P(\bar{C}) P(\bar{D})$\ $=1-(1-P(A))(1-P(B))$\ $(1-P(C))(1-P(D))$\ $=1-(1-0.4)(1-0.3)(1-0.2)(1-0.1)$ $=1-0.3024=0.6976$.\