Company X shipped 5 computer chips, 1 of which was defective. Company Y shipped 4, 2 defective. If chosen chip is defective, prob it came from Y?
- A. 2/9
- B. 4/9
- C. 2/3
- D. 1/2
Answer: C. 2/3
Explanation: P(D|X) = 1/5. P(D|Y) = 2/4 = 1/2. Assume P(X)=P(Y)=1/2 (randomly chosen). P(Y|D) = P(D|Y)P(Y) / (P(D|X)P(X) + P(D|Y)P(Y)) = (1/2 * 1/2) / (1/5 * 1/2 + 1/2 * 1/2) = (1/4) / (1/10 + 1/4) = (1/4) / (7/20) = 5/7. Wait. Question says 'If the chosen chip is found to be defective'. Are we choosing a company first or pooling all chips? 'randomly from the 9 chips shipped'. Total 9 chips. Total defective = 1+2=3. Chips from Y = 4. Defective from Y = 2. P(Y|Defective) = Defective_Y / Total_Defective = 2/3.