The following contingency table cross-classifies medical school faculty by the c

Question

The following contingency table cross-classifies medical school faculty by the characteristics gender and rank.

Male

G1

Female

G2

Professor

R1

Associate Professor

R2

Assistant Professor

R3

Instructor

R4

Other

R5

A) Find P(R2)

B) Find P(R2|G1)

C) Are events G1 and R2 independent? Show probability numbers that support your answer

D) Find P(R4 and G2)

E) Find P(R4 or G2)

F) Are events R4 and G2 mutually exclusive? Explain your answer

Male

G1

Female

G2

Total

Professor

R1

21,224 3,194 24,418

Associate Professor

R2

16,332 5,400 21,732

Assistant Professor

R3

25,888 14,491 40,379

Instructor

R4

5,775 5,185 10,960

Other

R5

781 723 1,504 Total 70,000 28,993 98,993

Explanation / Answer

A) P(R2) = 21732 / 98993 = 0.219

B) P(R2|G1) = 16332 / 98993 = 0.165

C) P(G1) = 70000 / 98993 = 0.707

P(R2) = 21732 / 98993 = 0.219

P(G1 AND R2) = 16332 / 98993 = 0.165

Clearly ,  P(G1 and R2) in not equal to P(G1) *  P(R2).

Therefore ,  events G1 and R2 are not independent.

D) P(R4 and G2) = 5185 / 98993 = 0.052

E) P(R4 or G2) = (10960 + 28993 - 5185) / 98993 = 0.351

F) P(R4 and G2) = 5185 /98993 = 0.052

   Clealy , P(R4 and G2) in not equal to 0.

Hence , events R4 and G2 are not mutually exclusive.

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