Summary Chapter 4 (SUT 2.1.1): Conditional Probabilities of a Two-way table

Chapter 4
Study Unit 2.1
PROBABILITY TESTING

, Study Unit 2.1.1
Conditional probabilities in a two-way table

The Definition of Conditional probability:
The probability of event A given that event B already occurred:
P( A ⋂ B)
P ( A|B )= where P( B)≠ 0
P(B)

Example pg. 203:
The police force consists of 1200 officers, 960 are men and 240 are women. Over the past the
past 2 years 324 have received promotions. The specific breakdown of promotions for male and
female is given in the table below. After reviewing the promotion record, a committee of
female officers raised a discrimination case on the basis that 2888 male officers had received a
promotion but only 36 female officers had received promotions. The police administration
argued that the relatively low number of promotions for females was due not to discrimination
but to the fact that relatively few females are members of the police force. Let us show how
conditional probability could be used to analyze the discrimination change.
Men Women
Total
Event M Event W
Promoted event A 288 36 324
C
Not promoted event A 672 204 876
960 240 1200

288
 P ( M ∩ A )= =0.24
1200
C 672
 P ( M ∩ A )= =0.56
1200
36
 P ( W ∩ A )= =0. 03
1200
C 204
 P (W ∩ A )= =0. 17
1200
Men Women
Total
Event M Joint
Eventprobabilities
W
Promoted event A 0.24 0.03 0.27 P(A)
Not promoted event
0.56 0.17 0.73 P(AC)
AC
0.80 0.20 1
P(M) P(W)




Marginal probabilities