Test by Bikram | Mock GATE | Test 2 | Question: 36

Question

Amazon shipped $5$ computer parts, $1$ of which was defective, and Flipkart shipped $4$ computer parts, $2$ of which were defective. One computer part is to be chosen uniformly at random from the $9$ parts shipped by the companies. If the chosen part is found to be defective,  the probability that the chip came from  Flipkart is _______.

Answer 1

P(Flipcart /defective) = n(Flipcart $\bigcap$ Defective) / n(Defective)
n(Flipcart $\bigcap$ Defective) = 2
n(Defective) = 3

P(Flipcart /defective) = (2 / 3) = 0.667

Answer 2

Given Data :

P(D/F) = 2/4 , P(F) = 4/9

P(D/A) = 1/5 , P(A) = 5/9

To Find : P(F/D)

Soln : Apply Bayes Theorem

P(F/D) = P(F$\cap$D) / P(D)

           = P(D/F) * P(F) / P(D)

           = P(D/F) * P(F) / (P(D/F) * P(F) + P(D/A) * P(A))

           = (2/4 * 4/9) / (2/4 * 4/9 + 1/5 * 5/9)

           = 2/9 / 3/9

           = .67

Comments

@Arjun sir, could you tell me what's wrong in this?

P(defective from amazon) is 1/5

P(defective from flipkart) is 2/4

P(given selected is defective and from flipkart) is 2/4 / (2/4+1/5) = 0.714

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For getting probability of defective, you cannot add the probabilities of defectives from Amazon and Flipkart. See the accepted answer now -- it is fairly straightforward here.