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A certain type of missile hits the target with probability p = 0.3. What is the least number of missiles should be fired so that there is at least an 80% probability that the target is hit?
- a)5
- b)6
- c)7
- d)None of the above
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A certain type of missile hits the target with probability p = 0.3. Wh...
Probability of hittiy the forget = 0.3
If'n' is the no. of times that the Missile is fired.
Probability of hitting at least once = 1-[1-0.3]n = 0.8
0.7n=0.2
n log 0.7 = log 0.2
⇒n=4.512
for n = 4 ; p < 0 . 8
taken = 5
If'n' is the no. of times that the Missile is fired.
Probability of hitting at least once = 1-[1-0.3]n = 0.8
0.7n=0.2
n log 0.7 = log 0.2
⇒n=4.512
for n = 4 ; p < 0 . 8
taken = 5
Most Upvoted Answer
A certain type of missile hits the target with probability p = 0.3. Wh...
To solve this problem, we can use the concept of the binomial distribution. The binomial distribution is used to model situations where there are only two possible outcomes, in this case, hitting or missing the target.
Let's denote the probability of hitting the target as p = 0.3 and the probability of missing the target as q = 1 - p = 0.7.
We want to find the least number of missiles that should be fired so that there is at least an 80% probability of hitting the target.
Let's denote the number of missiles fired as n.
To find the probability of hitting the target at least once in n missiles, we can use the complement rule. The complement of hitting the target at least once is missing the target every time.
The probability of missing the target in one missile is q = 0.7. The probability of missing the target in n missiles is q^n.
So, the probability of hitting the target at least once in n missiles is 1 - q^n.
We want this probability to be at least 80%, so we have the inequality:
1 - q^n ≥ 0.8
Let's solve this inequality for n:
1 - 0.7^n ≥ 0.8
0.7^n ≤ 0.2
Taking the logarithm of both sides:
log(0.7^n) ≤ log(0.2)
n * log(0.7) ≤ log(0.2)
n ≥ log(0.2) / log(0.7)
Using a calculator, we find that n ≥ 4.33.
Since n must be a positive integer, the least number of missiles that should be fired is 5.
Therefore, the correct answer is option A) 5.
Let's denote the probability of hitting the target as p = 0.3 and the probability of missing the target as q = 1 - p = 0.7.
We want to find the least number of missiles that should be fired so that there is at least an 80% probability of hitting the target.
Let's denote the number of missiles fired as n.
To find the probability of hitting the target at least once in n missiles, we can use the complement rule. The complement of hitting the target at least once is missing the target every time.
The probability of missing the target in one missile is q = 0.7. The probability of missing the target in n missiles is q^n.
So, the probability of hitting the target at least once in n missiles is 1 - q^n.
We want this probability to be at least 80%, so we have the inequality:
1 - q^n ≥ 0.8
Let's solve this inequality for n:
1 - 0.7^n ≥ 0.8
0.7^n ≤ 0.2
Taking the logarithm of both sides:
log(0.7^n) ≤ log(0.2)
n * log(0.7) ≤ log(0.2)
n ≥ log(0.2) / log(0.7)
Using a calculator, we find that n ≥ 4.33.
Since n must be a positive integer, the least number of missiles that should be fired is 5.
Therefore, the correct answer is option A) 5.
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A certain type of missile hits the target with probability p = 0.3. What is the least number of missiles should be fired so that there is at least an 80% probability that the target is hit?a)5b)6c)7d)None of the aboveCorrect answer is option 'A'. Can you explain this answer?
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A certain type of missile hits the target with probability p = 0.3. What is the least number of missiles should be fired so that there is at least an 80% probability that the target is hit?a)5b)6c)7d)None of the aboveCorrect answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about A certain type of missile hits the target with probability p = 0.3. What is the least number of missiles should be fired so that there is at least an 80% probability that the target is hit?a)5b)6c)7d)None of the aboveCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain type of missile hits the target with probability p = 0.3. What is the least number of missiles should be fired so that there is at least an 80% probability that the target is hit?a)5b)6c)7d)None of the aboveCorrect answer is option 'A'. Can you explain this answer?.
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