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A system consisting of n components functions if, and only if, at least one of n components functions. Suppose that all the n components of the system function independently, each with probability 3/4. If the probability of functioning of the system is 63./64, then the value of n is
- a)2
- b)4
- c)3
- d)5
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A system consisting of n components functions if, and only if, at leas...
Probability of the component to function (p) = 3/4
Probability of the component not to function (q) = 1/4
Probability of functioning the system = 63/64
⇒ Probability that at least one component function = 63/64
⇒ Probability that no component functions
Probability of the component not to function (q) = 1/4
Probability of functioning the system = 63/64
⇒ Probability that at least one component function = 63/64
⇒ Probability that no component functions
Most Upvoted Answer
A system consisting of n components functions if, and only if, at leas...
Given information:
- System consisting of n components functions only if at least one of n components functions.
- All n components function independently, each with probability 3/4.
- Probability of functioning of the system is 63/64.
To find: The value of n.
Solution:
Let's assume that the system does not function if k components fail.
From the given information, we know that the probability of any component failing is (1-3/4) = 1/4.
Using the above information, we can write the probability of k components failing as:
P(k components fail) = (1/4)^k
Now, we know that the system functions if at least one component functions. Therefore, the probability of the system functioning can be written as:
P(system functions) = 1 - P(all n components fail)
P(all n components fail) = P(n components fail) = (1/4)^n
Putting the given probability of the system functioning in the above equation, we get:
63/64 = 1 - (1/4)^n
Solving for n, we get n = 3.
Therefore, the value of n is 3.
Answer: Option C.
- System consisting of n components functions only if at least one of n components functions.
- All n components function independently, each with probability 3/4.
- Probability of functioning of the system is 63/64.
To find: The value of n.
Solution:
Let's assume that the system does not function if k components fail.
From the given information, we know that the probability of any component failing is (1-3/4) = 1/4.
Using the above information, we can write the probability of k components failing as:
P(k components fail) = (1/4)^k
Now, we know that the system functions if at least one component functions. Therefore, the probability of the system functioning can be written as:
P(system functions) = 1 - P(all n components fail)
P(all n components fail) = P(n components fail) = (1/4)^n
Putting the given probability of the system functioning in the above equation, we get:
63/64 = 1 - (1/4)^n
Solving for n, we get n = 3.
Therefore, the value of n is 3.
Answer: Option C.
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A system consisting of n components functions if, and only if, at least one of n components functions. Suppose that all the n components of the system function independently, each with probability 3/4. If the probability of functioning of the system is 63./64, then the value of n isa)2b)4c)3d)5Correct answer is option 'C'. Can you explain this answer?
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A system consisting of n components functions if, and only if, at least one of n components functions. Suppose that all the n components of the system function independently, each with probability 3/4. If the probability of functioning of the system is 63./64, then the value of n isa)2b)4c)3d)5Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A system consisting of n components functions if, and only if, at least one of n components functions. Suppose that all the n components of the system function independently, each with probability 3/4. If the probability of functioning of the system is 63./64, then the value of n isa)2b)4c)3d)5Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A system consisting of n components functions if, and only if, at least one of n components functions. Suppose that all the n components of the system function independently, each with probability 3/4. If the probability of functioning of the system is 63./64, then the value of n isa)2b)4c)3d)5Correct answer is option 'C'. Can you explain this answer?.
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