Section7.3 – Rules of Probability
1
Section 7.3
Rules of Probability
Let S be a sample space, E and F are events of the experiment then,
1.
0 <
P(E) <
1, for any event E.
2.
P(S) = 1
3.
If E and F are mutually exclusive, (E
I
F = Ø), then P(E
U
F) = P(E) + P(F).
(Note that this property can be extended to a finite number of events.)
4.
If E and F are not mutually exclusive, (E
I
F
≠
Ø), then
P(E
U
F) = P(E) + P(F) – P(E
I
F).
(Note that this property can be extended to a finite number of events.)
Example 1:
Let E and F be two events and suppose that P(E) = 0.37, P(F) = 0.3 and
)
(
F
E
P
I
=.08.
Find:
a.
P(E
U
F)
b.
)
(
F
E
P
c
I
5.
Rule of Complements:
If E is an event and E
c
denotes the complement of E then
P(E
c
) = 1 – P(E).
Example 2:
Let E and F be two events and suppose that P(E) = 0.54, P(F) = 0.56 and
)
(
F
E
P
I
=.18.
Find:
a.
P(F
c
)
b.
c
F
E
P
)
(
I
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2
Example 3:
Let E and F be events of a sample space S.
Let P(E
c
) = 0.69, P(F) = 0.36
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 Fall '10
 AbdelnourAhmedZaid
 Math, Mutually Exclusive, Probability, Probability theory, Public utility, sample space S., space S. Let

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