An Investment Firm Has Classified Its Clients According to Their

question 91

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.
Express each of the following probabilities in words.
a. P(A | B).
b. P(B | A).
c. P(A | $\bar { B }$ ).
d. P( $\bar A$ | B).

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Definitions:

Output

The quantity of goods or services produced by a firm, sector, or economy within a certain period.

Overhead Costs

Expenses not directly tied to the production of goods or services, such as rent, utilities, and administrative salaries.

Newspaper Industry

Refers to the sector of the economy that is engaged in the production and distribution of newspapers, involving both print and, increasingly, digital platforms.

Shrink

The reduction in inventory due to factors such as theft, damage, or errors in record-keeping.