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

Question

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

Quizplus · Accepted Answer

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

An Investment Firm Has Classified Its Clients According to Their