An Investment Firm Has Classified Its Clients According to Their

question 92

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

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Definitions:

Onc/o

A prefix in medical terminology denoting relation to tumors or cancer.

Combining Form

A form used in the construction of medical and scientific terminology, typically a root with a vowel at the end that allows it to be connected to other terms.

Tumor

An abnormal mass of tissue that forms when cells grow and divide more than they should or do not die when they should.

Malignant

Referring to a severe and progressively worsening condition, especially concerning tumors that are cancerous and can spread to other body parts.