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1.017/1.010 Class 4
Joint Probability, Independence, Repeated Trials
Joint Probabilities and Independence
Joint probability
of 2 events
A
and
B
defined in the same sample space
(probability that outcome lies in
A
and
B
):
P
(
AB
)
= P
(
C
)
;
where event
C = A
B= AB
I
If
A
and
B
are
independent
then:
P
(
AB
)
= P
(
A
)
P
(
B
)
Note that
mutually exclusive events are not independent
since if one occurs
we know the other has not.
Example:
Consider the following events
A
and
B
defined from a die toss experiment with
outcomes {
1, 2, 3, 4, 5, 6
}
A
= {2, 4 ,6}
B
= {1, 2 ,3, 4}
Then:
P
(
A
) = 1/2 ,
P
(
B
)
= 2/3, P(
AB
) = 2/6 =
P
(
A
)
P
(
B
)
So
A
and
B
are independent.
Composite experiments
Related experiments are often conducted in a sequence.
For example, suppose we toss a fair coin (with 2 equally likely outcomes {
H T
})
and then throw a fair die (with 6 equally likely outcomes {
1, 2, 3, 4, 5, 6
}).
This
process can be viewed as two separate experiments
E
1
and
E
2
with different
sample spaces.
Or … it can be viewed as a single composite experiment
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 Spring '05
 GeorgeKocur

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