An Investment Firm Has Classified Its Clients According to Their

question 90

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.
Find the following probabilities.
a. P(A | B).
b. P(B | A).
c. P(A | $\bar { B }$ ).
d. P( $\bar A$ | B).

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Definitions:

Union Pension Funds

Retirement fund pools managed by labor unions on behalf of their members, providing benefits upon retirement based on the collective contributions and investments.

Corporate Strategies

Plans or methods implemented by corporations to achieve specific business goals, including growth, market expansion, and competitiveness.

Investment Strategies

Plans or approaches designed to allocate financial assets in a way that achieves financial goals.

Social Agenda

A set of priorities or objectives set by an organization or government, focusing on social issues such as welfare, health, and social justice.