2.5. SOME BASIC OPERATIONS OF PROBABILITY 33
Example 2.10
In a class survey, the percentage of five options: “Strongly agree,” “Agree,” “No opinion,” “Dis-
agree,” and “Strongly disagree” on a survey question are 24%, 48%, 8%, 15%, and 5%. What is
the percentage of the answers with at least “Agree” on the survey question?
Solution:
Since the option of “Strongly agree” and “Agree” are a mutually exclusive event, we have:
P
.
‘‘Strongly agree” [ ‘‘Agree”
/
D P
.
‘‘strongly agree”
/
C P
.
‘‘Agree”
/
D 0:24 C 0:48 D 0:72:
2.5.2 PROBABILITY OF AN EVENT IN A FINITE SAMPLE SPACE
Assume that event A in a finite sample space contain n sample points (outcomes), that is,
A D
f
E
1
; : : : ; E
n
g
. Since each sample point is a mutually exclusive event with any other sample
point (outcome), the probability of an event A in a finite sample space is
P
.
A
/
D P
.
f
E
1
; : : : ; E
n
g
/
D
iDn
X
iD1
P
.
E
i
/
: (2.16)
Example 2.11
In an experiment of rolling a dice, calculate the probability of event A D
f
1; 4; 5
g
.
Solution:
Since the event A contains three sample points, the probability of each sample point in
rolling a dice experiment will be 1/6. So the probability P
.
A
/
is
P
.
A
/
D P
.
f
1; 4; 5
g
/
D P
.
f
1
g
/
C P
.
f
4
g
/
C P
.
f
5
g
/
D
1
6
C
1
6
C
1
6
D
1
3
:
Example 2.12
e outcome of an experiment of rolling a dice twice will be the sum of showing numbers.
Calculate the probability of an event A D
f
4; 7
g
.
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