An Investment Firm Has Classified Its Clients According to Their

question 97

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 $\cup$ B).
b. P(A $\cap$ B).
c. P(A $\cap$$\bar { B }$ ).
d. P( $\bar A$$\cup$ $\bar { B }$ ).

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Definitions:

Employment Discrimination

Unfair treatment of employees or job applicants based on race, gender, age, religion, or other non-job-related factors.

Similar Productivity Characteristics

Refers to entities or products that share common features in terms of efficiency, output, or performance.

Employment Discrimination

Unfair or prejudicial treatment of employees or job applicants based on characteristics such as race, gender, or age.

Earnings Gap

The difference in average earnings between different groups in the economy, often discussed in terms of gender, race, or education level.