The following table provides the data from a sample of course instructors from a

Question

The following table provides the data from a sample of course instructors from a local college, noting their home faculty (instructors can only teach in one faculty) and their educational level. Total Facult Sciences Humanities Degree Bachelors 22 Masters PhD Other Total 110 27 6 121 220 Based on the data in the contingency table, find the following probabilities (please show your work for part marks): a) If one of the instructors is selected at random what is the probability that the person is b) If one of the instructors is selected at random what is the probability that the individual is c) If one of the instructors is selected at random what is the probability that they have a d) If one of the instructors is selected at random what is the probability that they are not e) If two instructors are selected at random what is the probability that both have a Master's f) If 58% of the Humanities instructors are male, what is the probability that an instructor from Humanities and has a Bachelor's degree? from the sciences, given that they have a "Masters" degree? Masters degree, given that they are in the Humanities? from Sciences, given they don't have a PhD? degree and both individuals are from Sciences? selected at random will be a female Humanities instructor?

Explanation / Answer

a) P( Humanities and Bachelors) = 55/220=0.25

b) P( Science/Masters) = 66/110=0.6

c) P( Masters/Humanitis) = 44/121=4/11=0.3636

d) P( Not science/ Not masters) = (121-21)/(220-27) = 0.5181

e)Probaility = (66/220)^2 = 0.09

f)P( Humanities and Female) = 0.42* 121/220 = 0.231

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