Quantitative Methods MCQ - Quantitative Methods Section 2

36 Which of the following statements about dependent and independent events is most likely true?

A
P(A)P(B) is used to determine the joint probability of the two events, A and B, whether they are dependent or independent.
B
P(A)P(B) is used to determine the joint probability of the two events, A and B, that are independent.
C
The two events are independent if the occurrence of one event is related to the occurrence of the other.

The multiplication rule is applied only when the two events A and B are independent.

37 Two events, A and B, are independent. Given that P(A) ≠ P(B), the probability of P(A│B) is most likely:

Since the events are independent, P(A|B) = P(A) and P(B|A) = P(B).

38 An analyst is analyzing the prospects of survival of ShopKart, an ecommerce retailer over the next six months. The retailer’s survival depends on the growth in customer base. The analyst assigns probabilities to three possible scenarios and estimates the probability of closing down for each of them.

Scenario	Probability of scenario	Probability of closing down
Decrease in customer base	30%	60%
Maintaining the customer base 30%	50%	30%
Increase in customer base	20%	10%

Based on the analyst’s estimates, the probability that ShopKart will not close down in the next six months is closest to:

Using the total probability rule, the unconditional probability of closing down is given by: (0.3) (0.6) + (0.5) (0.3) + (0.2) (0.1) = 0.35 The probability that ShopKart will not close down is, 1 – 0.35 = 0.65 = 65%

39 Which of the following is used to determine the unconditional probability, given conditional probabilities?

The total probability rule is used to determine the unconditional probability, given conditional probabilities.

40 Conditional expectation is least likely used in investments to determine which of the following?

With Option A we are considering the expected value of EPS if interest rates increase. This requires the use of conditional probability. Option C has the term „different scenarios‟ which implies the use of conditional probabilities.