SATHEE: Probability 3 Question 43

Probability 3 Question 43

43. 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 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?

(1981, 2M)

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Answer:

Correct Answer: 43. $\frac{1}{1260}$

Solution:

Let $P (H_{1}) = 0.4, P (H_{2}) = 0.3, P (H_{3}) = 0.2, P (H_{4}) = 0.1$

$P$ (gun hits the plane)

$\begin{aligned} = 1 - P (gun does not hit the plane) \\ = 1 - P ({\bar{H}}_{1}) \cdot P ({\bar{H}}_{2}) \cdot P ({\bar{H}}_{3}) \cdot P ({\bar{H}}_{4}) \\ = 1 - (0.6) (0.7) (0.8) (0.9) = 1 - 0.3024 = 0.6976 \end{aligned}$

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Probability 3 Question 43

43. 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 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?

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43. 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 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?