ISRO | ISRO CS 2007 | Question 33

Company X shipped 5 computer chips, 1 of which was defective and company Y shipped 4 computer chips, 2 of which were defective. One computer chip is to be chosen uniformly at a random from the 9 chips shipped by the companies. If the chosen chip is found to be defective, what is the probability that the chip came from the company Y?
(A) 2/9
(B) 4/9
(C) 2/3
(D) 1/2


Answer: (C)

Explanation: Probability that chip came chosen from company X = 5/9
Probability that chip came chosen from company Y = 4/9

Number of Defective chips from company X = 1
Number of Defective chips from company Y = 2

Probability that chip is defective from company X = 5/9 * 1/5
Probability that chip is defective from company Y = 4/9 * 2/4
Probability that chip is defective = 5/9 * 1/5 + 4/9 * 2/4

Given chip is defective, probability that it came from the company Y = P(Defective Company Y)/ P(Defective)
= (4/9 * 2/4) / (5/9 * 1/5 + 4/9 * 2/4)
= 2/3

Option (C) is correct.


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