In a large companv it is known that 40% of the employees are college graduates a

Question

In a large companv it is known that 40% of the employees are college graduates and that 60% of the employees are women. Furthermore,-5% of the college graduates are women. If an emplovee is selected at random. points) Q1.1: What is the probability that the empiovee is both a college graduate and a women? Q12: If a women is selected. what is the probability that she is a college graduate? Q1.3: What is the probability of selecting either a coilege yopduate or a women? Q1.4: Are the events 'college graduate and women dependent or independent? Why?

Explanation / Answer

Given,
P(College graduate) = 0.4, P(Woman) = 0.6, P(Woman | College Graduate) = 0.75

1) P(College graduate and woman) = P(Woman | College graduate) * P(College graduate) = 0.75 * 0.4 = 0.3

2) P(College graduate | Woman) = P(College graduate and woman)/ P(Woman) = 0.3/0.6 = 0.5

3) P(College graduate OR woman) = P(Woman) + P(College graduate) - P(Woman and college graduate)
= 0.6 + 0.4 - 0.3 = 0.7

4) Dependent, If they were independent, then P(College graduate | Woman) = P(College graduate)

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