Page 16 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 2 Probability

(b) The simple events in the sample space and their corresponding probabilities
are listed in the following table:
Event First coin Second coin P(E)
E 1 H H 1
4
E H T 1
2 4
E T H 1
Penerbitan Pelangi Sdn Bhd. All Rights Reserved.
3 4
E T T 1
2 4 4

(c) Let F = event of observing exactly one head in the two tosses.
The probability of observing exactly one head in the two tosses is,
F = {HT, TH}

P(F) = 2
4
= 1
2

Example 17

3 students are chosen from a group of 10 students consisting of 7 boys and 3 girls to represent a school
in chess competition. If the selection is merely based on random picking, find the probability that the
representatives are formed by
(a) 2 boys and 1 girl,
(b) at least 2 girls.

10
Solution: (a) There are C = 10! = 10 × 9 × 8 = 120 combinations by taking
3 (10 – 3)! 3! 3 × 2 × 1

3 from 10 students.
There are C × C = 7 × 6 × 3 = 63 combinations by exactly taking 2
7
3
2 1 2 × 1 1
boys and 1 girl from the group.
Hence, the probability that the representatives are formed by exactly 2 boys
and 1 girl is 63 = 21 .
120 40

(b) The selection could be either 2 girls and 1 boy or 3 girls and no boys.
So, the number of combinations of 2 girls and 1 boy or 3 girls and no boys
= C × C + C × C
7
3
3
7
2 1 3 0
= 3 × 7 + 1 × 1

= 22
The probability that the representatives are formed by at least 2 girls is
22 = 11 .
120 60

84

02 STPM Math(T) T3.indd 84 28/10/2021 10:21 AM