An Investment Firm Has Classified Its Clients According to Their

question 96

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.
Are A and B independent events? Explain.

---

Definitions:

Sales Price

The amount of money charged for a product or service, which can vary based on demand, market conditions, and production costs.

Production Cost

The total cost incurred by a business to produce goods or services, including labor, materials, and overhead.

Special Order

An order for goods or services that is outside the scope of regular operations, often requiring customization or special handling.

Capacity

The highest level of production a business can maintain to produce a good or offer a service.