Quantitative Methods MCQ - Quantitative Methods Section 2

31 The probability of event A is 80%. The probability of event B is 20%. The joint probability of AB is 35%. The probability that A or B occurs or both occur is closest to:

P(A or B) = P(A) + P(B) – P(AB) = 50 + 20 –5 = 65%.

32 A and B are two independent events. The probability of event A is 0.5 and the probability of event B is 0.4. The joint probability of A and B is closest to:

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.

33 From the past records of AB Financial Training, the passing rates for Level I exam and CTP exam have been 70% and 60% respectively. Analysis indicates that among the people who have passed CTP, 50% have also passed CFA Level I. What is the passing rate of CTP among people who have also passed CFA Level I before?

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%

34 A company has two bottle producing machines, one old and one new. The older machine produces 10% defective bottles, whereas the new machine produces 4% defective bottles only. Additionally, the new machine uses latest technology to produce 5 times as many bottles as the older machine. Given that the bottle was produced by the new machine, what is the probability that it is not defective?

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.

35 A and B are independent events. Which of the following conditions is least likely true regarding the probability of the independent events?

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.