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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A table of joint probabilities is shown below,regarding the instructors at the University of Michigan,where the events Ai(i = 1,2,3)and Bj (j = 1,2)are defined as follows: A1 = Full professor,A2 = Associate professor,A3 = Assistant professor,B1 = Male instructor,and B2 = Female instructor.
THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A table of joint probabilities is shown below,regarding the instructors at the University of Michigan,where the events A<sub>i</sub>(i = 1,2,3)and B<sub>j</sub> (j = 1,2)are defined as follows: A<sub>1</sub> = Full professor,A<sub>2</sub> = Associate professor,A<sub>3</sub> = Assistant professor,B<sub>1</sub> = Male instructor,and B<sub>2</sub> = Female instructor.    -Calculate P(A<sub>3</sub> ∣ B<sub>1</sub>).
-Calculate P(A3 ∣ B1).


Definitions:

Hawthorne Effect

The phenomenon where individuals modify an aspect of their behavior in response to their awareness of being observed.

Study Participation

The involvement of individuals as subjects in research to gather information and data for the purpose of advancing knowledge.

Bureaucracies

Administrative systems organized into a hierarchy of departments and offices, operating under a set of rules and regulations to ensure consistency and impartiality.

Behavior Patterns

Recurrent ways of acting or responding that are characteristic of an individual or group.

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