An Investment Firm Has Classified Its Clients According to Their

question 54

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:

Sales Representatives

Individuals who represent a company by selling its products or services to customers, often directly.

Undue Influence

A situation in which an individual is able to persuade another's decisions due to the relationship between the two parties, often undermining the independence of the decision.

Property Worth

The monetary value of real estate or personal property, determined by various factors including location, condition, and market trends.

Embarrassment

A feeling of self-consciousness, shame, or awkwardness that occurs when a person's dignity is wounded.