GATE Exam  >  GATE Questions  >  In a factory, two machines M1 and M2 manufact... Start Learning for Free
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?
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.
Explore Courses for GATE exam

Similar GATE Doubts

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?
Question Description
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?.
Solutions 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 English & in Hindi are available as part of our courses for GATE. Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of 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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an ample number of questions to practice 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? tests, examples and also practice GATE tests.
Explore Courses for GATE exam
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev