I have a quiz tomorrow and this is one of the exercises that I should know how to solve..
I need details on how it is solved please..


EX.4
The personnel department of an insurance company has compiled data regarding promotion, classified by gender. Is promotion and gender dependent on one another?

Manager Promoted (E) Not promoted (?) Total
Male (A) 46 184 230
Female (?) 8 32 40
Total 54 216 270

Let us check if P(E|A)=P(E). If this equality holds, there is no difference in probability of promotion between a male and a female manager.

-using the table in Ex.4 find the following:

- an employee is selected at random from this company find the following:

1. what is the probability that he is a male ?

2. what is the probability that she is a female and not promoted?

3. what is the probability that she is a female given that she is promoted?

4. are the two events male and promoted disjoint? Explain.

4. are the two events male and promoted independent? Explain.

Manager... Promoted (E)... Not promoted (E with a bar)... Total
Male (A)... 46... 184... 230
Female (A bar)... 8... 32... 40
Total... 54... 216... 270

1. Take total males divided by total people.

2. Take the total females who didn't get promoted, divide by total people.

3. Take the total promoted females, divide by total people who got promoted.

4. It is asking you if being male and being promoted exist or not. If it exist, then it is not disjoint.

5. This relates back to the initial question. Is being a male, gender dependent? Check for the suggested equality.