An Investment Firm Has Classified Its Clients According to Their

question 52

Essay

An investment firm has classified its clients according to their gender and the composition of their investment portfolios (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 $$\begin{array} { | l | c | c | c | } \hline \text { Gender } & \text { Bonds } & \text { Stocks } & \text { Balanced } \\\hline \text { Male } & 0.18 & 0.20 & 0.25 \\\hline \text { Female } & 0.12 & 0.10 & 0.15 \\\hline\end{array}$$ 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 A and $\bar { B }$ mutually exclusive events? Explain.

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Definitions:

Referent Power

A form of influence and authority derived from the charisma and interpersonal relationships of the power-holder, rather than formal positions.

Coercive Power

Refers to the ability of a person or group to enforce obedience from others through threats, punishment, or sanctions.

Legitimate Power

Authority that is accepted and recognized as rightfully held by an individual or organization, often through a formal position or role.

Legitimate Power

A form of authority where power is derived from a recognized and accepted position or role within a social structure.