An investment firm has classified its clients according to their gender and the

Question

An investment firm has classified its clients according to their gender and the composition of their investment portfolia (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table: Portfolio Composition Gender Male Female Balanced 0.25 0.15 Bonds 0.18 0.12 Stocks 0.20 0.10 One client is selected at random, and two events A and B are defined as follows A: The client selected is male B: The client selected has a balanced portfolio Are the events A and B independent? Events A and B are dependent Events A and B are independent Events A and B are mutually exclusive cannot be determined with given information

Explanation / Answer

P(A) = 0.18 + 0.2 + 0.25 = 0.63

P(B) = 0.25 + 0.15 = 0.4

P(A and B) = 0.25

P(A) * P(B) = 0.63 * 0.4 = 0.252

Since P(A and B) is not equal to P(A) * P(B), A and B are not independent events.

Option-A)

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