Page 21 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 2 Probability

(e) Since the events E and E make up the whole of the possibility space, hence,
2
1
E and E are exhaustive events.
1
2
(f) For exhaustive events E and E , P(E  E ) = 1
2
1
1
2
For equally probable outcomes P(E ) = P(E ),
1
2
P(E ) + P(E ) = 1
1 2
2P(E ) = 1
1
P(E ) = 1 = P(E )
1 2 2
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Probability of the union of events 2
In Example 22 we conducted an experiment by tossing a die. Event B was “obtaining a four” and event D
was “obtaining an odd number”. The probability of event B, P(B), is 1 and the probability of event D, P(D),
6
is 3 or 1 . Suppose we want to find the probability of tossing an odd number or four, which is denoted
2
6
by P(B  D).
We notice that events B and D are mutually exclusive. Hence,
P(B  D) = n(B  D) = n(B) + n(D)
n(S) n(S)
= n(B) + n(D)
n(S) n(S)
= P(B) + P(D)
= 1 + 1 = 2
6 2 3

Example 24

It is found that out of 100 students of a school, 65 students go to school by bus, 15 students walk to
school and the remaining 20 students go to school by other transportations. If a student is randomly
selected from this group of 100 students, what is the probability that the student selected either goes to
school by bus or walks to school?
Solution: Let event B be “the student selected goes to school by bus” and
event W be “the student selected walks to school”.
The two events are mutually exclusive as the selected student cannot go to school
by two different means at the same time.

Thus, we have P(B  W) = P(B) + P(W)
= 65 + 15
100 100
= 4
5

If two events A and B are mutually exclusive, the probability of A or B occurring is
P(A  B) = P(A) + P(B)

This is the addition rule for mutually exclusive events:

89

02 STPM Math(T) T3.indd 89 28/10/2021 10:21 AM