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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. The probability that the gun hits the plane is_____
Correct answer is between '0.69,0.7'. Can you explain this answer?
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Verified Answer
An anti-aircraft gun can take a maximum of 4 shots at an enemy plane m...
Let p1 = 0.4, p2 = 0.3, p3 = 0.2 and p4 = 0.1
P(the gun hits the plane) = P(the plane is hit at least once)
= 1 – P(the plane is hit in none of the shots)
= 1− (1−p1) (1−p2) (1−p3) (1−p4)
= 1− (0.6 × 0.7 × 0.8 × 0.9)
= (1− 0.3024) = 0.6976
= 1− (0.6 × 0.7 × 0.8 × 0.9)
= (1− 0.3024) = 0.6976
Most Upvoted Answer
An anti-aircraft gun can take a maximum of 4 shots at an enemy plane m...
Solution:
To find the probability that the gun hits the plane, we can use the complement rule -
P(hit) = 1 - P(miss)
where P(miss) is the probability that all 4 shots miss the plane.
Probability of all 4 shots missing the plane:
P(miss) = 0.6 x 0.7 x 0.8 x 0.9
= 0.3024
Using the complement rule,
P(hit) = 1 - P(miss)
= 1 - 0.3024
= 0.6976
Therefore, the probability that the gun hits the plane is 0.6976, which is between 0.69 and 0.7.
Explanation:
- An anti-aircraft gun has 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.
- To find the probability that the gun hits the plane, we use the complement rule - P(hit) = 1 - P(miss), where P(miss) is the probability that all 4 shots miss the plane.
- Probability of all 4 shots missing the plane is calculated by multiplying the probabilities of missing the plane at each shot.
- Using the complement rule, we get the probability that the gun hits the plane.
- The calculated probability is between 0.69 and 0.7.
To find the probability that the gun hits the plane, we can use the complement rule -
P(hit) = 1 - P(miss)
where P(miss) is the probability that all 4 shots miss the plane.
Probability of all 4 shots missing the plane:
P(miss) = 0.6 x 0.7 x 0.8 x 0.9
= 0.3024
Using the complement rule,
P(hit) = 1 - P(miss)
= 1 - 0.3024
= 0.6976
Therefore, the probability that the gun hits the plane is 0.6976, which is between 0.69 and 0.7.
Explanation:
- An anti-aircraft gun has 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.
- To find the probability that the gun hits the plane, we use the complement rule - P(hit) = 1 - P(miss), where P(miss) is the probability that all 4 shots miss the plane.
- Probability of all 4 shots missing the plane is calculated by multiplying the probabilities of missing the plane at each shot.
- Using the complement rule, we get the probability that the gun hits the plane.
- The calculated probability is between 0.69 and 0.7.
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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. The probability that the gun hits the plane is_____Correct answer is between '0.69,0.7'. Can you explain this answer?
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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. The probability that the gun hits the plane is_____Correct answer is between '0.69,0.7'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about 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. The probability that the gun hits the plane is_____Correct answer is between '0.69,0.7'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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. The probability that the gun hits the plane is_____Correct answer is between '0.69,0.7'. Can you explain this answer?.
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. The probability that the gun hits the plane is_____Correct answer is between '0.69,0.7'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about 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. The probability that the gun hits the plane is_____Correct answer is between '0.69,0.7'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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. The probability that the gun hits the plane is_____Correct answer is between '0.69,0.7'. Can you explain this answer?.
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