An Investment Firm Has Classified Its Clients According to Their

question 91

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.
Express each of the following probabilities in words.
a. P(A | B).
b. P(B | A).
c. P(A | $\bar { B }$ ).
d. P( $\bar A$ | B).

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Definitions:

Echo Virus

A type of enterovirus that can cause a variety of diseases, ranging from mild febrile illness to severe conditions like meningitis.

Code L13.0

A specific code possibly used in a medical classification system to indicate a particular diagnosis or condition, but without context, the exact definition cannot be provided.

Dermatosis Herpetiformis

A chronic skin condition featuring blisters filled with a watery fluid, often associated with gluten sensitivity.

Duhring's Disease

Another name for Dermatitis Herpetiformis, a chronic blistering skin condition linked to gluten sensitivity.