Quantitative Methods MCQ - Quantitative Methods Section 2

26 A and B are independent events. P(AB), the joint probability of events A and B is best denoted by:

According to the multiplication rule of probabilities, the joint probability of A and B can be expressed as: P(AB) = P(A|B) * P(B) It is given that A and B are independent events and hence P(A|B) = P(A). P(AB) = P(A) * P(B).

27 AB & Co. has issued two callable bonds with a maturity of 2 and 5 years respectively. The probability that Bond A will be called is 60% and the probability that Bond B will be called is 50%. The probability that at least one of the bonds will be called is closest to:

The probability that at least one of the bonds will be called can be calculated using the Addition rule of probability which is: P(A or B) = P(A) + P(B) – P(A and B) where P(A and B) is P(A) * P(B) P(A or B) = 0.6 + 0.5 - 0.6 * 0.5 = 0.8.

28 The probability of stock A going up is 0.6 and the probability of Stock B going up is 0.2. The probability that both stocks will go up is 0.15. What is the probability that Stock A will go up or Stock B will go up or both will go up?

Whenever or is used, use the addition rule for probabilities to calculate the probability of either of the events occurring or that both will occur: P(A or B) = P(A) + P(B) – P(AB) P(A or B) = 0.6 + 0.2 – 0.15 = 0.65.

29 The probability of an above average economic growth for a country is 0.35. The probability that GE stock will appreciate given the above average economic growth is 0.60.The joint probability of an above average economic growth and appreciation of GE stock is closest to:

The joint probability can be computed using the multiplication rule: P (AB) = P(A B) P(B) where P(A B) is the conditional probability of A given that B has occurred. If, A refers to the probability that that GE stock will appreciate and B refers to the probability that the economic growth will be above average, then the joint probability is: 0.60 * 0.35 = 0.21.

30 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:

The probability that at least one of two events will occur is the sum of the probabilities of the separate events less the joint probability of the two events. P(A or B) = P(A) + P(B) – P(AB) 80% = 70% + 20% – P(AB); therefore, P(AB) = 10%.