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1. You are working as an analyst for a policy center. You are being asked to ser

ID: 3062710 • Letter: 1

Question

1. You are working as an analyst for a policy center. You are being asked to serve as a consultant for a large metropolitan area. They are facing a possible legal battle over discrimination in promotion practices You are provided the following information: Promoted 288 36 324 Not Promoted 672 204 876 Total 960 240 1200 Male Female A. Build a probability table from the data above. B. What is the probability that the employee is a male? C. What is the probability that the employee is a female? D. What is the probability that the employee is a man and is promoted? E. What is the probability that the employee is a female and is promoted? F. What types of probability are we referencing in parts C and D above? (Hint: are they prior, conditional, joint, posterior or marginal probabilities) G. What type of probability would you be interested in here? (Hint: Probability that employee is a male given that he was promoted or the probability that an employee is promoted given that he is a male) H. Draw the probability tree for this problem. Make sure you include priors, conditionals and joint probabilities I. What conclusions would you draw from your analysis?

Explanation / Answer

A. Probability of a randomly selected person being male and promoted = 288/1200= 0.24

Probability of a randomly selected person being male and not promoted = 672/1200= 0.56

Probability of a randomly selected person being a female and promoted = 36/1200= 0.03

Probability of a randomly selected person being female and not promoted = 204/1200= 0.17

The probability table looks like below:

Promoted Not Promoted Total

Male 0.24 0.56 0.80

Female 0.03 0.17 0.20

0.27 0.73 1.00

B. Probability that the employee is a male = 0.80 (from the above table).

C. Probability that the employee is a female = 0.20

D. Probability that the employee is a man and promoted = 0.24

E. Probability that the employee is a female and promoted = 0.03

F. These are joint probabilities.

G. Since the issue is about discrimination in promotion practices, we would be interested in the probability that the employee is promoted, given that he is a male.