1. Basic Conditional Probability
In 5.4 we first introduce the conditional probability rule.
P
(
A

B
) =
)
(
)
(
B
P
B
A
P
P(
A

B
) means “what is the probability of A given B occurs”. If events A and B are
not
independent
we call the events
dependent.
The property P(A  B)
≠
P(A) will be true if
the events are dependent. In other words the fact B occurs effects the probability A
occurs.
An example can be motivated by a contingency (or joint frequency) table:
Example 1)
We survey 100 HS senior males about their college plans and their family background.
We examine how a father’s education may affect a son’s plan.
Let A = father is college educated
B
= A
C
= father is not college educated
D = son goes to college
E =
D
C
= son doesn’t go to college
Father College Educated
Father Not College Educated
Son goes to College
30
10
Son doesn’t go to
College
20
40
If we simply ask the question P(D) “the probability the son goes to college” we see that
30 + 10 sons go to college while 20 + 40 do not. So 40 of 100 sons go to college.
P(D) =
40
.
0
100
40
=
On the other hand if the father is college educated the plans of the son seems to be
effected.
Of 50 college educated fathers 30 of the sons go to college.
P(D  A) =
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Stefeni
 Conditional Probability, Probability, Probability space, Father Not College Educated

Click to edit the document details