An Investment Firm Has Classified Its Clients According to Their

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. $\quad P ( \bar { A } \cup \bar { B } )$ .