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Question
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?
Solution
\[P \left( \text{ gun hits the plane } \right) = 1 - \left( \text{ gun does not hit the plane } \right)\]
\[ \Rightarrow P\left( A \right) = 1 - P\left( \bar{A} \right)\]
\[\text{ Now } , \]
\[ \Rightarrow P\left( \bar{A} \right) = \left( 1 - 0 . 4 \right)\left( 1 - 0 . 3 \right)\left( 1 - 0 . 2 \right)\left( 1 - 0 . 1 \right)\]
\[ = 0 . 6 \times 0 . 7 \times 0 . 8 \times 0 . 9\]
\[ = 0 . 3024\]
\[ \therefore P\left( A \right) = 1 - 0 . 3024\]
\[ = 0 . 6976\]
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