An Investment Firm Has Classified Its Clients According to Their

question 9

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. $\quad P ( A \cup B )$ .
b. $P ( A \cap B )$ .
c. $P ( A \cap \bar { B } )$ .
d. $\quad P ( \bar { A } \cup \bar { B } )$ .

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Definitions:

HR Self-Service

Technology-enabled tools that allow employees to manage their own HR-related tasks without the need to interact directly with HR staff.

Enterprise Portals

Centralized online platforms that provide employees within an organization with access to a wide range of internal and external resources, information, and services.

Human Resource Planning

The process of forecasting an organization's future human resource needs and developing plans to ensure that a suitable workforce is in place.

Mobile Technology

A set of technologies that enables communication, computing, and the sharing of data with mobile devices like smartphones and tablets.