Question

In a recent survey, human resource directors were surveyed to find out attitude towards job candidates showing exposure to Ethics courses. In that survey, 36% of the directors identify as female. We also know that of the female directors, 90% think it is important to take an ethics course and 25% of the male directors did NOT think it was important.

a. What is the probability that out of everybody, a director is both female and does think it is important to have an Ethics course?

b. What is the probability that a director is both male and does not think it is important or both of these events occur?

c. What is the probability that a director identifies as female, given that they think an ethics course is unimportant?

Answer 1

a) Probability that a director is both female and thinks that it is important to have an Ethics course =

P(director being female) * P(The female directors thinks that the ethics course is important)

= 0.36*0.9

= 0.324.

b) Probability that a director is both male and does not think it is important to take ethics course =

= P(director is a male)* P(the male director does not think it is important to take ethics course)

=(1-P(director is a female) * P(the male director does not think it is important to take ethics course)

= (1-0.36) * 0.25

= 0.16.

c) Probability that a director is identified as female, given that the director thinks that the course in not important =

Probability that a director thinks that the course is not important =

Probability that a male director doesn’t think that the course is important + Probability that a female director doesn’t think that the course is important

= 0.64*0.25 + 0.36*(1-0.90)

= 0.16 + 0.036

= 0.196.

So, the required probability that the director is identified as female, when it is given that the director thinks that the ethics course is not important =

= P(Director is female and thinks the ethics course is not important) / P(Director thinks that the ethics course is not important)

= 0.036 / 0.196

= 0.184

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