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 portfolio (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

Bonds

Stocks

Balanced

Male

0.18

0.20

0.25

Female

0.12

0.10

0.15

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

Gender

Bonds

Stocks

Balanced

Male

0.18

0.20

0.25

Female

0.12

0.10

0.15

Explanation / Answer

Here P(A)=0.63

And P(B)=0.40

A and B are not independent as P(A)*P(B) is not zero

In other words male's portfolio being balanced is not as likely as a portfolio being balanced.

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