Quantitative Methods - Quantitative Methods Section 2
- Option : A
- Explanation : A and B are two independent events, their joint probability is equal to the product of their individual probabilities, so joint probability = 0.5 × 0.4 = 0.2.
- Option : B
- Explanation : Data given in the question: P(CFA) = 70%, P(CTP) = 60% P(CTP | CFA) = P(CTP CFA) / P(CFA) We have to find the passing rate of CTP giving members who have passed the CFA exams as well. P(CFA and CTP) = P (CTP CFA) = P (CFA | CTP) * P(CTP) = 0.5 * 0.6 = 0.3 P(CTP | CFA) = P(CTP and CFA) / P(CFA) = 0.3 / 0.7 = 0.428 or 42.8%
- Option : B
- Explanation : The question is asking for the probability of a bottle produced by the new machine which is not defective. In the question, the probability of defective is given as 4% and therefore, the probability of not defective will be 1 - 0.04 = 0.96.
- Option : C
- Explanation : Note that A and B are independent events, and not mutually exclusive events. It is possible that both the independent events occur. Hence, the joint probability, P (AB) is not necessarily 0. Options A and B are correct for independent events.
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