Question

A metropolitan police force consists of 1,400 officers, 450 belonging to racial minorities. Over the past two years, 370 officers on the police force received promotions. A committee of racial minorities raised a discrimination case stating that of those promoted in the last two years only 42 were racial minorities. Construct a contingency table and answer the following questions.

a. What is the probability that a randomly selected officer is not promoted in the last two years?

b. What is the probability that a randomly selected officer is a racial minority?

c. What is the probability that a randomly selected officer is a racial minority and not promoted in the last two years?

d. What is the probability that a randomly selected officer is a racial minority or not promoted in the last two years?

e. Given a randomly selected officer is a racial minority what is the probability that he or she was not promoted in the last two years?

f. Based on these probabilities does the discrimination case raised by the committee have prima facie merit? Explain why using probabilities.

Answer 1

A contingency table as below:

(A) The probability that a randomly selected officer is not promoted in the last two years = 1030/ 1400

= 0.736

(B) The probability that a randomly selected officer is a racial minority = 450/ 1400

= 0.321

(C) The probability that a randomly selected officer is a racial minority and not promoted in the last two years = 408/ 1400

= 0.291

(D)

  The probability that a randomly selected officer is a racial minority or not promoted in the last two years = (450/ 1400) + (1030/ 1400) - (408/ 1400)

= 0.766

(E)

A randomly selected officer is a racial minority what is the probability that he or she was not promoted in the last two years = 408/ 1400

= 0.291