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.

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 from Humanities and has a Bachelor's degree?
b) If one of the instructors is selected at random what is the probability that the individual is from the sciences, given that they have a "Masters" degree?
c) If one of the instructors is selected at random what is the probability that they have a Masters degree, given that they are in the Humanities?
d) If one of the instructors is selected at random what is the probability that they are not from Sciences, given they don't have a PhD?
e) If two instructors arc selected at random what is the probability that both have a Master's degree and both individuals are from Sciences?
f) If 58% of the Humanities instructors are male, what is the probability that an instructor selected at random will be a female Humanities instructor?

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Degree Faculty Sciences Total Humanities 55 44 Bachelors Masters 22 77 110 66 6. PhD 21 27 Other 6. Total 121 220 99