SOLUTION: The classification of faculty at a college is indicated in the following table: Male Female Total Professor 12 3 15 Associate professor 15 9 24 Assistant professor 18 8 26

Question 851027: The classification of faculty at a college is indicated in the following table:
Male Female Total
Professor 12 3 15
Associate professor 15 9 24
Assistant professor 18 8 26
Instructor 20 15 35
Total 65 35 100
a) If a committee of three faculty members is selected at random what is the probability that:
i) All females.
ii) A professor and two associate professor .
b) If a faculty member is selected at random from this college, find the probability that:
i) The faculty is male, given that the faculty is instructor.
ii) The faculty is not professor given that the faculty is female.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The classification of faculty at a college is indicated in the following table:
.........................Male Female Total
Professor................12 3 15
Associate professor......15 9 24
Assistant professor..... 18 8 26
Instructor........ 20 15 35
Total............. 65 35 100
a) If a committee of three faculty members is selected at random what is the probability that:
i) All females.::
# of ways to select 3 female faculty members:: 35C3
# pf ways to select 3 random faculty members:: 100C3
------------
Ans:: 35C3/100C3 = 0.0405
ii) A professor and two associate professor
# of ways to select a professor (15) and 2 assoc. profs (24C2)::
# of ways to select 3 random faculty members:: 100C3
-----------
Ans:: [15*24C2]/100C3 = 0.0256
b) If a faculty member is selected at random from this college, find the probability that:
i) The faculty is male, given that the faculty is instructor.
Ans:: (# of ways to succeed)/(# of random selection) = 20/35
ii)The faculty is not professor given that the faculty is female
Ans:: (# of ways to succeed)/(# of random selections) = 32/35
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Cheers,
Stan H.
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