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If it known that the probability of a missile hitting a target is 1/8, what is the probability that out of 10 missiles fired, at least 2 will hit the target?
- a)0.4258
- b)0.3968
- c)0.5238
- d)0.3611
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
If it known that the probability of a missile hitting a target is 1/8,...
Solution:
The given problem is an example of the binomial distribution.
Formula:
The probability of getting r successes in n independent trials, where p is the probability of success and q is the probability of failure, is given by the binomial distribution formula:
P(r) = nCr * p^r * q^(n-r)
Where,
n = number of trials
r = number of successes
p = probability of success
q = probability of failure = 1-p
nCr = number of combinations of n things taken r at a time = n! / (r! * (n-r)!)
Given:
p = 1/8
q = 1 - p = 7/8
n = 10
To find:
The probability that at least 2 missiles out of 10 will hit the target.
Solution:
Let X be the number of missiles that hit the target.
We need to find P(X ≥ 2).
P(X ≥ 2) = 1 - P(X < />
P(X < 2)="P(X" =="" 0)="" +="" p(x="" />
P(X = 0) = nC0 * p^0 * q^(n-0) = 1 * (1/8)^0 * (7/8)^10 = 282475249/1073741824
P(X = 1) = nC1 * p^1 * q^(n-1) = 10 * (1/8)^1 * (7/8)^9 = 1200626325/4294967296
P(X < 2)="(282475249" +="" 1200626325)="" 4294967296="" />
P(X ≥ 2) = 1 - P(X < 2)="2811865722/7818749351" ≈="" />
Therefore, the probability that at least 2 missiles out of 10 will hit the target is 0.3611 or option (d).
The given problem is an example of the binomial distribution.
Formula:
The probability of getting r successes in n independent trials, where p is the probability of success and q is the probability of failure, is given by the binomial distribution formula:
P(r) = nCr * p^r * q^(n-r)
Where,
n = number of trials
r = number of successes
p = probability of success
q = probability of failure = 1-p
nCr = number of combinations of n things taken r at a time = n! / (r! * (n-r)!)
Given:
p = 1/8
q = 1 - p = 7/8
n = 10
To find:
The probability that at least 2 missiles out of 10 will hit the target.
Solution:
Let X be the number of missiles that hit the target.
We need to find P(X ≥ 2).
P(X ≥ 2) = 1 - P(X < />
P(X < 2)="P(X" =="" 0)="" +="" p(x="" />
P(X = 0) = nC0 * p^0 * q^(n-0) = 1 * (1/8)^0 * (7/8)^10 = 282475249/1073741824
P(X = 1) = nC1 * p^1 * q^(n-1) = 10 * (1/8)^1 * (7/8)^9 = 1200626325/4294967296
P(X < 2)="(282475249" +="" 1200626325)="" 4294967296="" />
P(X ≥ 2) = 1 - P(X < 2)="2811865722/7818749351" ≈="" />
Therefore, the probability that at least 2 missiles out of 10 will hit the target is 0.3611 or option (d).
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If it known that the probability of a missile hitting a target is 1/8,...
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If it known that the probability of a missile hitting a target is 1/8, what is the probability that out of 10 missiles fired, at least 2 will hit the target?a)0.4258b)0.3968c)0.5238d)0.3611Correct answer is option 'D'. Can you explain this answer?
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If it known that the probability of a missile hitting a target is 1/8, what is the probability that out of 10 missiles fired, at least 2 will hit the target?a)0.4258b)0.3968c)0.5238d)0.3611Correct answer is option 'D'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If it known that the probability of a missile hitting a target is 1/8, what is the probability that out of 10 missiles fired, at least 2 will hit the target?a)0.4258b)0.3968c)0.5238d)0.3611Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If it known that the probability of a missile hitting a target is 1/8, what is the probability that out of 10 missiles fired, at least 2 will hit the target?a)0.4258b)0.3968c)0.5238d)0.3611Correct answer is option 'D'. Can you explain this answer?.
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