2.5. SOME BASIC OPERATIONS OF PROBABILITY 35
Example 2.13
Among the graduate students of a university, 42% receive loans, 25% receive teaching assis-
tantships, and 14% receive both. What % of students receive either a loan or an assistantship?
Solution:
Let the events A and B represent receiving a loan and research assistantships, respectively. Ac-
cording to the given information, we have:
P
.
A
/
D 0:42I P
.
B
/
D 0:25 and P
.
A B
/
D 0:14:
erefore, the probability of students receives either a loan or an assistantship will be:
P
.
A [B
/
D P
.
A
/
C P
.
B
/
P
.
A B
/
D 0:42 C 0:25 0:14 D 0:53 D 53%:
Example 2.14
A student could select a science course denoted as event A; a math course denoted as event B
or none of these two courses. From the registering information, 40% of students have chosen a
science course, 50% a math course, and 75% at least one of a science and a math course. Calculate
the percentage of students who select both a science and a math course.
Solution:
According to the given information, we have:
P
.
A
/
D 0:40I P
.
B
/
D 0:50 and P
.
A [B
/
D 0:75:
According to Equation (2.15), we have
P
.
A B
/
D P
.
A
/
C P
.
B
/
P
.
A [B
/
D 0:40 C 0:50 0:75 D 0:15:
2.5.4 PROBABILITY OF A COMPLEMENTARY EVENT
Assume that the probability of an event A in a sample space is P .A/, then the probability of
the complementary event A is:
P
A
D 1 P
.
A
/
: (2.19)
Example 2.15
e outcome of an experiment of rolling a dice twice will be the sum of showing numbers.
Calculate the probability of the sum showing numbers not equal to 5.
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