4. (2opts)The following table shows promotion status of police officers over 2 y

Question

4. (2opts)The following table shows promotion status of police officers over 2 years period. PROMOTION STATUS OF POLICE OFFICERS OVER THE PAST TWO YEARS Men Women Total Promoted Not Promoted 672 288 324 36 204 Total 960 240 1200 Let Ma event officer is a man, A: event officer is promoted, W-event officer is a woman, A": event officer is not promoted a. Create a joint probability table. b. What are the marginal probabilities P(A) and P(W) Prw)- c. Find the conditional probability P (A|M) d. What is the probability P (M UA)? mean but different standard deviations are shown here.

Explanation / Answer

a)dividing each cell with 1200 ; below is joint probability table:

b)

P(A) =0.27

P(W)=0.2

c)

P(A|M)=P(A n M)/P(M)= 0.24/0.8 =0.3

d)P(M U A) =P(M)+P(A) -P(M n A) =0.8+0.27-0.24=0.83

men women Total promoted 0.24 0.03 0.27 not promoted 0.56 0.17 0.73 Total 0.8 0.2 1

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