An Investment Firm Has Classified Its Clients According to Their

question 21

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 $\bar { B }$ independent events? Explain.

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Definitions:

Violent Behavior

A pattern of conduct marked by acts of aggression or physical force that can result in harm or injury to individuals or property.

Frustration-Aggression Principle

A hypothesis suggesting that aggression is the result of blocking, or frustrating, a person's efforts to achieve a goal.

Implicit Associations

Unconscious or automatic associations between different concepts in one's memory, which can influence thought and behavior without the individual's awareness.

Outgroup Homogeneity

The perception that members of an outgroup (a group one does not belong to) are more similar to each other than they actually are or compared to members of the ingroup.