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Introduction to Business Statistics
Lecture 3A
Conditional Probability and Statistical Independence
Example
(
Sex Discrimination
): A company of 1200 employees (960
men and 240 women) promoted 288 men and 36 women last year. Is a
man more likely to be promoted than a woman? Is a promoted person
more likely to be a man? Is there a ground to claim sex discrimination?
Let us first find the probability “the randomly selected employee was
promoted last year on the condition that the employee is male”
Let
T
be the event that the selected employee was promoted last year
and
M
be the event that the selected employee is male. Then we write
the conditional probability as
P
(
T

M
)
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z
Conditional probability is the revised proportion based on the
subpopulation (a different sample space).
z
What is the size of male subpopulation? (960) In the subpopulation
how many were promoted? (288) So the revised proportion is
288/960 = 0.3.
z
The other way to find the conditional probability is through the
following definition using probabilities in the original sample space.
3
.
0
8
.
0
24
.
0
1200
/
960
1200
/
288
)
(
)
M
(
)

(
=
=
=
∩
=
M
P
T
P
M
T
P
;
15
.
0
2
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 Fall '08
 HU
 Business

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