An Investment Firm Has Classified Its Clients According to Their

question 90

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.
Find the following probabilities.
a. P(A | B).
b. P(B | A).
c. P(A | $\bar { B }$ ).
d. P( $\bar A$ | B).

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Definitions:

Common Method

A widely used or accepted technique or procedure for achieving a task or solving a problem.

Common Shares

Shares to which no preferential rights or privileges are attached.

Broadly Held Corporation

A corporation with a large number of shareholders, spreading ownership widely among individuals.

Closely Held Corporation

A corporate entity characterized by a small group of shareholders, often with family members holding a majority of the stock.