An Investment Firm Has Classified Its Clients According to Their

question 93

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:

Folkways

Norms for routine or casual interaction that guide everyday behavior in a society.

Corporate Social Responsibility

A business approach that contributes to sustainable development by delivering economic, social, and environmental benefits for all stakeholders.

Ethical

Pertaining to or dealing with morals or the principles of morality; concerned with the distinction between good and evil or right and wrong behavior.

Philanthropic

Pertaining to the act of contributing to the welfare of others, often through charitable donations or actions by individuals or organizations.