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.:: 
# of ways to select 3 female faculty members:: 35C3 
# pf ways to select 3 random faculty members:: 100C3
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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
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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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