The following contingency table cross-classifies medical school faculty by the c
ID: 3430554 • Letter: T
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
TotalProfessor
R1
21,224 3,194 24,418Associate Professor
R2
16,332 5,400 21,732Assistant Professor
R3
25,888 14,491 40,379Instructor
R4
5,775 5,185 10,960Other
R5
781 723 1,504 Total 70,000 28,993 98,993Explanation / 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.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.