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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. -Show that P(A<sub>1</sub> ∣ B<sub>1</sub>)+ P(A<sub>2</sub> ∣ B<sub>1</sub>)+ P(A<sub>3</sub> ∣ B<sub>1</sub>)= 1
-Show that P(A1 ∣ B1)+ P(A2 ∣ B1)+ P(A3 ∣ B1)= 1

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