Page 18 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 2 Probability

Example 19

A die is tossed.
(a) Calculate the probability of,
(i) obtaining an odd number,
(ii) getting an even number.
(b) Show the validity of the rule for complementary events.

Solution: (a) The sample space for tossing a die is S = {1, 2, 3, 4, 5, 6}.
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(i) Let A be the event of obtaining an odd number.
Event A = {1, 3, 5}
2 P(A) = 3
6
= 1
2
(ii) Let B be the event of getting an even number.
Event B = {2, 4, 6}.
P(B) = 3
6
= 1
2
(b) P(A) + P(B) = 1 + 1
2 2
= 1
We have thus illustrated the rule of complementary events.

Example 20

A letter is randomly selected from the alphabet. Find the probability of not getting a vowel.
Solution: Let A be the event of getting a vowel. There are 5 vowels {a, e, i, o, u} and a
total of 26 letters in the alphabet. Thus,

P(A) = n(A) = 5 .
n(S) 26
The event of not getting a vowel is the complement of the event A. By the rule
of complementary events, we have
P(A) = 1 – P(A)
5
= 1 – 26
= 21
26
Alternatively, we can find the probability directly by counting the letters that are
not vowels. So, n(A) = 21 and P(A) = 21 .
26

Note: Sometimes using complementary events can make the probability calculation easier.

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02 STPM Math(T) T3.indd 86 28/10/2021 10:21 AM