GATE | GATE CS 2012 | Question 63

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


Answer: (B)

Explanation:

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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