In a given scenario - 1. Suppose that 9% of all employees in a given company are locals, 14% are men, and 18% have graduate degrees from top 10 schools. Let A, B and C be, respectively, the events that a randomly selected individual from this population is local, a man, and has graduated from top 10 school.
1) Do you believe that A, B and C are independent events? Explain why or why not.
2) Assuming A, B and C are independent events, find the probability that a randomly selected manager from this company is a non-local female and has earned an top-10 graduate business school. (only consider two ethnicities here- local and non-local, and two genders- male and female)
For question 1- I think that these are dependent as it is likely that out of 18% top ten group few could be men (given 14% are men), but I am not 100% sure. Can anyone pitch in and clarify? Also I cannot conclude if A is independent or not. Thanks!