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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>2</sub> ∣ B<sub>1</sub>).
-Calculate P(A2 ∣ B1).


Definitions:

Variable Costs

refer to expenses that change in proportion to the activity of a business, such as costs for raw materials or production volume.

Fixed Costs

Costs that do not change with the level of output produced, such as rent or salaries.

AVC Curve

The Average Variable Cost (AVC) Curve is a graphical representation showing the relationship between a firm's output level and its average variable cost.

Break-Even

The point at which total costs equal total revenue, resulting in no net loss or gain for a business.

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