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GATE CS 2012 · General Aptitude

Question 63

MCQPrinted as GA Q.632 marksWrong answer: −2/3Medium (estimate)

Question

An automobile plant contracted to buy shock absorbers from two suppliers XX and YY. XX supplies 60% and YY 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 XX's shock absorbers, 96% are reliable. Of YY's shock absorbers, 72% are reliable.

The probability that a randomly chosen shock absorber, which is found to be reliable, is made by YY is

Choose one option
Official answer and solution
Official answer
B
From
Official GATE 2012 answer key

Solution

Apply Bayes' Theorem to compute the posterior probability that a reliable shock absorber came from supplier Y.

  1. Prior probabilities:
P(X)=0.60,P(Y)=0.40P(X) = 0.60, \quad P(Y) = 0.40
  1. Likelihood of being reliable (RR):
P(R∣X)=0.96,P(R∣Y)=0.72P(R \mid X) = 0.96, \quad P(R \mid Y) = 0.72
  1. Total probability of reliability P(R)P(R):
P(R)=0.60×0.96+0.40×0.72=0.576+0.288=0.864P(R) = 0.60 \times 0.96 + 0.40 \times 0.72 = 0.576 + 0.288 = 0.864
  1. By Bayes' Theorem:
P(Y∣R)=P(Y)⋅P(R∣Y)P(R)=0.2880.864=13≈0.3333P(Y \mid R) = \frac{P(Y) \cdot P(R \mid Y)}{P(R)} = \frac{0.288}{0.864} = \frac{1}{3} \approx 0.3333
  1. Rounding to three decimal places gives 0.3340.334 (Option B).
Final answer

B

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper
GATE 2012 Computer Science and Information Technology (CS)
Question
63 of 65, printed as GA Q.63
Section
General Aptitude

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