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).

---

Definitions:

Cognitive Attribution Biases

Tendencies to make systematic errors in judgment when evaluating reasons for one's own and others' behaviors.

Depression

An emotional health issue distinguished by an ongoing low spirit or disinterest in activities, significantly affecting daily operations.

Heterotypic Continuity

Heterotypic Continuity refers to the concept that underlying psychological issues can manifest as different behavioral problems at different stages of development.

ODD

Oppositional Defiant Disorder, a behavioral disorder in children marked by defiant, disobedient, and hostile behaviors towards authority figures.