This preview shows pages 1–2. Sign up to view the full content.
AMS 310
Chapter 3.6 3.7
3.6. Conditional Probability
Definition of conditional probability
:
If
A
and
B
are any events in
S
and
P(B)
is not equal to zero, the conditional probability of
A
given
B
is
P
A
B
P
A
B
P
B
(

)
(
)
(
)
.
=
∩
EXAMPLE
: What is the probability that the number of dots on a fair die is even given that the number of spots showing is 3
or
less?
Definition of independent events
: The event
A
is independent of the event
B
if
P(AB)=P(A)
.Equivalently
)

(
)

(
B
A
P
B
A
P
=
)
.
EXAMPLE
:
Suppose P(A and B) =1/8 and P(B) =1/6 and P(A)=1/2. Are A and B independent?
Suppose A and B are
independent. Then what is the value of P(A
∩
B)?
Theorem 3.8. General multiplication rule of probability
.
If
A
and
B
are
any
events in
S
, then P(A
∩
B) = P(AB)P(B) =P(BA)P(A) for P(A), P(B)
≠
0
EXAMPLE (
Using the General Multiplication Rule): We are told that we will get a job if we are in the top 10% of scores on two
tests. Suppose however, the probability of being in the top 10% on test 2 given we are in the top 10% on test 1 equals 90%.
What
is the probability we will get the job?
Theorem 3.9. Product rule of probability for independent events
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.
 Fall '03
 Mendell

Click to edit the document details