Homework SourseThe following contingency table crossclassifies medical scho
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 |
Solution
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.
