An Investment Firm Has Classified Its Clients According to Their

question 76

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:

Bank Account

An account held by an individual or business with a financial institution, allowing for the deposit and withdrawal of funds.

Physical Custody

The actual possession or direct control of tangible assets, documents, or securities.

Asset Records

Documentation that details the acquisition, valuation, and disposal of assets owned by an individual or organization.

External Auditors

Independent professionals outside of the organization who examine the company's financial statements to ensure accuracy and compliance with accounting standards.