An Investment Firm Has Classified Its Clients According to Their

question 6

Short Answer

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

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Definitions:

Customer Value

The perception of what a product or service is worth to a customer compared to the alternatives.

Value Proposition

A promise of value to be delivered, communicated, and acknowledged by a customer, distinguishing a product or service from competitors.

Market Segments

Division of a broader market into smaller, homogenous groups of consumers with similar needs, wants, or demographic profiles.

Market Segmentation

The practice of dividing a target market into smaller, more defined categories based on various characteristics.