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An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies 60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test.
The ones that pass the quality test are considered reliable. Of X’s shock absorbers, 96% are reliable. Of Y’s shock absorbers, 72% are reliable.
The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y is
  • a)
    0.288
  • b)
    0.334
  • c)
    0.667
  • d)
    0.720
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
An automobile plant contracted to buy shock absorbers from two supplie...
Probability that the absorber is reliable = 0.96*0.6 + 0.72*0.4 
                                          = 0.576 + 0.288


Probability that  the absorber is from y and reliable = 
            (Probability that is made by Y)  X (Probability that it is reliable)
           = 0.4 * 0.72 
           = 0.288

The probability that randomly picked reliable absorber is from y = 
    (Probability that  the absorber is from y and reliable) / (>Probability that the absorber is reliable )
   = (0.288)/ (0.576 + 0.288) 
   =  0.334 
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Most Upvoted Answer
An automobile plant contracted to buy shock absorbers from two supplie...
's shock absorbers, 96% are reliable, while only 72% of Y's shock absorbers are reliable.

To find the overall reliability of the shock absorbers, we need to calculate the weighted average of the reliability of X and Y's shock absorbers.

Weighted average reliability = (reliability of X * % supplied by X) + (reliability of Y * % supplied by Y)

= (0.96 * 0.60) + (0.72 * 0.40)

= 0.576 + 0.288

= 0.864

Therefore, the overall reliability of the shock absorbers is 0.864 or 86.4%.
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An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test.The ones that pass the quality test are considered reliable. Of X’s shock absorbers, 96% are reliable.Of Y’s shock absorbers, 72% are reliable.The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Yisa)0.288b)0.334c)0.667d)0.720Correct answer is option 'B'. Can you explain this answer?
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An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test.The ones that pass the quality test are considered reliable. Of X’s shock absorbers, 96% are reliable.Of Y’s shock absorbers, 72% are reliable.The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Yisa)0.288b)0.334c)0.667d)0.720Correct answer is option 'B'. 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 An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test.The ones that pass the quality test are considered reliable. Of X’s shock absorbers, 96% are reliable.Of Y’s shock absorbers, 72% are reliable.The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Yisa)0.288b)0.334c)0.667d)0.720Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test.The ones that pass the quality test are considered reliable. Of X’s shock absorbers, 96% are reliable.Of Y’s shock absorbers, 72% are reliable.The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Yisa)0.288b)0.334c)0.667d)0.720Correct answer is option 'B'. Can you explain this answer?.
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