An Investment Firm Has Classified Its Clients According to Their

question 92

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:

Sunk Costs

Costs that have already been incurred and cannot be recovered.

Foregone Opportunities

Benefits or earnings that are missed out on when choosing one alternative over another.

Accounting Costs

The actual expenses and cash outlays that a business incurs, which are recorded in its financial statements.

Dental Floss

A thin filament used to remove food and dental plaque from between teeth in areas a toothbrush is unable to reach.