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.
1
)
(
0
≤
≤
E
P
, for any event E.
2.
1
)
(
=
S
P
3.
)
(
)
(
)
(
)
(
F
E
P
F
P
E
P
F
E
P
∩

=
∪
Note: If E and F are mutually exclusive (i.e.,
=
∩
F
E
Ø), then the rule becomes:
)
(
)
(
)
(
F
P
E
P
F
E
P
=
∪
4.
)
(
1
)
(
E
P
E
P
c

=
Example:
A die is cast once.
a) What is the probability that the number is even or greater than 3?
E: the number is odd; {1,3,5}
F: the number is greater than 4; {5,6}
F
E
∩
={5}
P(E)=3/6=1/2.
P(F)=2/6=1/3.
6
/
1
)
(
=
∩
F
E
P
.
3
2
6
1
3
1
2
1
)
(
)
(
)
(
)
(
=

+
=
∩

+
=
∪
F
E
P
F
P
E
P
F
E
P
b) What is the probability that the number is 2 or 4?
P({2})=1/6,
P({4})=1/6.
The events are mutually exclusive.
3
1
6
1
6
1
)
(
)
(
)
(
=
+
=
+
=
∪
F
P
E
P
F
E
P
c) What is the probability that the number is not 2?
P({2})=1/6;
6
5
6
1
1
)
}
2
({
=

=
c
P
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Section7.3 – Rules of Probability
2
Example 1:
A box contains 10 cards numbered from 1 to 10. 3 of these cards are red (numbered
1 to 3) and 7 of them are blue (numbered 4 to 10). A card is chosen at random.
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 Spring '08
 CONSTANTE
 Math, Mutually Exclusive, Probability, Probability theory, Probability space

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