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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?
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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Verified Answer
In a factory, two machines M1 and M2 manufacture 60% and 40% of the au...
Let E1 be the machine M1 manufacture auto companies
Let E2 be the event of machine M2 manufacture auto companies
Given P(E1 )= 60% = 60/100
Let E2 be the event of machine M2 manufacture auto companies
Given P(E1 )= 60% = 60/100
A randomly draw on auto component from the lot is sound defective the
probability it was manufactured by M2 is P(E2 / A) we have
probability it was manufactured by M2 is P(E2 / A) we have
Most Upvoted Answer
In a factory, two machines M1 and M2 manufacture 60% and 40% of the au...
To solve this problem, we can use Bayes' theorem. Bayes' theorem allows us to calculate the probability of an event happening given that another event has already occurred.
Let's define the events:
A: The component is defective
B: The component was manufactured by M2
We are given the following probabilities:
P(M1) = 0.6 (M1 manufactures 60% of the components)
P(M2) = 0.4 (M2 manufactures 40% of the components)
P(A|M1) = 0.02 (2% of M1 components are defective)
P(A|M2) = 0.03 (3% of M2 components are defective)
We need to find P(B|A), the probability that the component was manufactured by M2 given that it is defective.
Using Bayes' theorem, we have:
P(B|A) = (P(A|B) * P(B)) / P(A)
Let's calculate each term:
P(A|B) = P(A intersection B) / P(B)
= P(A|M2) * P(M2) / P(M2)
= 0.03 * 0.4 / 0.4
= 0.03
P(B) = P(M2) = 0.4
P(A) = P(A intersection M1) + P(A intersection M2)
= P(A|M1) * P(M1) + P(A|M2) * P(M2)
= 0.02 * 0.6 + 0.03 * 0.4
= 0.012 + 0.012
= 0.024
Now, we can substitute these values back into Bayes' theorem:
P(B|A) = (P(A|B) * P(B)) / P(A)
= (0.03 * 0.4) / 0.024
= 0.012 / 0.024
= 0.5
Therefore, the probability that the defective component was manufactured by M2 is 0.5 or 50%. Hence, the correct answer is option 'C'.
Let's define the events:
A: The component is defective
B: The component was manufactured by M2
We are given the following probabilities:
P(M1) = 0.6 (M1 manufactures 60% of the components)
P(M2) = 0.4 (M2 manufactures 40% of the components)
P(A|M1) = 0.02 (2% of M1 components are defective)
P(A|M2) = 0.03 (3% of M2 components are defective)
We need to find P(B|A), the probability that the component was manufactured by M2 given that it is defective.
Using Bayes' theorem, we have:
P(B|A) = (P(A|B) * P(B)) / P(A)
Let's calculate each term:
P(A|B) = P(A intersection B) / P(B)
= P(A|M2) * P(M2) / P(M2)
= 0.03 * 0.4 / 0.4
= 0.03
P(B) = P(M2) = 0.4
P(A) = P(A intersection M1) + P(A intersection M2)
= P(A|M1) * P(M1) + P(A|M2) * P(M2)
= 0.02 * 0.6 + 0.03 * 0.4
= 0.012 + 0.012
= 0.024
Now, we can substitute these values back into Bayes' theorem:
P(B|A) = (P(A|B) * P(B)) / P(A)
= (0.03 * 0.4) / 0.024
= 0.012 / 0.024
= 0.5
Therefore, the probability that the defective component was 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 manufacturedby 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 manufacturedby 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 manufacturedby 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 manufacturedby 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 manufacturedby 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 manufacturedby 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 manufacturedby M2?a)0.35b)0.45c)0.5d)0.4Correct answer is option 'C'. Can you explain this answer?.
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