An Investment Firm Has Classified Its Clients According to Their

question 40

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:

Ethical Guidelines

Rules and standards designed to guide appropriate conduct, particularly in scholarly and professional contexts.

Physiological Recording

The measurement and documentation of bodily functions, such as heart rate, brain activity, and muscle tension, often used in psychological research.

Subject

An individual or entity being observed or experimented upon in scientific or academic studies.

Violent Movie

A film genre characterized by depictions of physical aggression, harm, or force against others.