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In a factory, two machines M1 and M2 manufacture 60% and 40% of the autocomponents respectively. Out of the total production, 2% of M1 and 3% of M2 are found to be defective. If a randomly drawn autocomponent from the combined lot is found defective, what is the probability that it was manufactured by M2?
- a)0.35
- b)0.45
- c)0.5
- d)0.4
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
In a factory, two machines M1 and M2 manufacture 60% and 40% of the au...
Solution:
Let A be the event that the component is manufactured by M1 and B be the event that the component is manufactured by M2. Let D be the event that the component is defective.
Given, P(A) = 0.6, P(B) = 0.4, P(D|A) = 0.02 and P(D|B) = 0.03.
Finding P(D):
Using the law of total probability, we can find the probability of a defective component.
P(D) = P(D|A)P(A) + P(D|B)P(B)
P(D) = (0.02)(0.6) + (0.03)(0.4)
P(D) = 0.024
Finding P(B|D):
Using Bayes' theorem, we can find the probability that the component is manufactured by M2 given that it is defective.
P(B|D) = P(D|B)P(B)/P(D)
P(B|D) = (0.03)(0.4)/0.024
P(B|D) = 0.5
Therefore, the probability that the defective component is manufactured by M2 is 0.5 or 50%. Hence, the correct answer is option C.
Let A be the event that the component is manufactured by M1 and B be the event that the component is manufactured by M2. Let D be the event that the component is defective.
Given, P(A) = 0.6, P(B) = 0.4, P(D|A) = 0.02 and P(D|B) = 0.03.
Finding P(D):
Using the law of total probability, we can find the probability of a defective component.
P(D) = P(D|A)P(A) + P(D|B)P(B)
P(D) = (0.02)(0.6) + (0.03)(0.4)
P(D) = 0.024
Finding P(B|D):
Using Bayes' theorem, we can find the probability that the component is manufactured by M2 given that it is defective.
P(B|D) = P(D|B)P(B)/P(D)
P(B|D) = (0.03)(0.4)/0.024
P(B|D) = 0.5
Therefore, the probability that the defective component is manufactured by M2 is 0.5 or 50%. Hence, the correct answer is option C.
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In a factory, two machines M1 and M2 manufacture 60% and 40% of the autocomponents respectively. Out of the total production, 2% of M1 and 3% of M2 are found to be defective. If a randomly drawn autocomponent from the combined lot is found defective, what is the probability that it was manufactured by M2?a)0.35b)0.45c)0.5d)0.4Correct answer is option 'C'. Can you explain this answer?
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In a factory, two machines M1 and M2 manufacture 60% and 40% of the autocomponents respectively. Out of the total production, 2% of M1 and 3% of M2 are found to be defective. If a randomly drawn autocomponent from the combined lot is found defective, what is the probability that it was manufactured by M2?a)0.35b)0.45c)0.5d)0.4Correct 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 In a factory, two machines M1 and M2 manufacture 60% and 40% of the autocomponents respectively. Out of the total production, 2% of M1 and 3% of M2 are found to be defective. If a randomly drawn autocomponent from the combined lot is found defective, what is the probability that it was manufactured by M2?a)0.35b)0.45c)0.5d)0.4Correct 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 In a factory, two machines M1 and M2 manufacture 60% and 40% of the autocomponents respectively. Out of the total production, 2% of M1 and 3% of M2 are found to be defective. If a randomly drawn autocomponent from the combined lot is found defective, what is the probability that it was manufactured by M2?a)0.35b)0.45c)0.5d)0.4Correct answer is option 'C'. Can you explain this answer?.
In a factory, two machines M1 and M2 manufacture 60% and 40% of the autocomponents respectively. Out of the total production, 2% of M1 and 3% of M2 are found to be defective. If a randomly drawn autocomponent from the combined lot is found defective, what is the probability that it was manufactured by M2?a)0.35b)0.45c)0.5d)0.4Correct 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 In a factory, two machines M1 and M2 manufacture 60% and 40% of the autocomponents respectively. Out of the total production, 2% of M1 and 3% of M2 are found to be defective. If a randomly drawn autocomponent from the combined lot is found defective, what is the probability that it was manufactured by M2?a)0.35b)0.45c)0.5d)0.4Correct 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 In a factory, two machines M1 and M2 manufacture 60% and 40% of the autocomponents respectively. Out of the total production, 2% of M1 and 3% of M2 are found to be defective. If a randomly drawn autocomponent from the combined lot is found defective, what is the probability that it was manufactured by M2?a)0.35b)0.45c)0.5d)0.4Correct answer is option 'C'. Can you explain this answer?.
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