CA Foundation P3 · Chapter 15 · Question 8 of 9
Machines A and B produce 60% and 40% of a factory's output. 2% of A's output and 5% of B's output is defective. An item chosen at random is found defective. The probability that it was produced by machine B is:
Test yourself: pick an answer
Reveal answer & explanation
Correct answer: A) 0.625
Explanation
By Bayes' theorem: P(D|A)P(A) = 0.02 x 0.6 = 0.012 and P(D|B)P(B) = 0.05 x 0.4 = 0.020. Total P(D) = 0.032. P(B|D) = 0.020/0.032 = 0.625. 0.375 is P(A|D), and 0.032 is the total probability of a defective item.
More Probability MCQs
- Q1Two fair dice are thrown. The probability that the sum of the numbers is 8 is:
- Q2A bag contains 5 red and 7 blue balls. Two balls are drawn at random without replacement. The probability that both are red is:
- Q3If P(A) = 0.5, P(B) = 0.4 and P(A ∩ B) = 0.2, then P(A ∪ B) is:
- Q4The odds in favour of an event are 3 : 5. The probability of the event is:
- Q5If P(A) = 0.6, P(B) = 0.5 and P(A ∪ B) = 0.8, then P(A | B) is: