Counting and Probability Practice Questions
Matric (South Africa) · Matric Mathematics · 143 free MCQs with instant results and detailed explanations.
143
Total
44
Easy
79
Medium
20
Hard
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Sample Questions from Counting and Probability
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Q1
Easy
If a box contains 5 red balls and 3 green balls, what is the probability of picking a green ball?
A.
1/2
B.
3/8
C.
3/5
D.
5/8
Show Answer & Explanation
Correct Answer: B
The total number of balls is 8 (5 red + 3 green). The probability of picking a green ball is the number of green balls (3) divided by the total number of balls (8), giving a probability of 3/8.
Q2
Easy
A bag contains 5 red balls and 3 blue balls. If one ball is drawn at random, what is the probability that it is blue?
A.
0.375
B.
0.25
C.
0.5
D.
0.2
Show Answer & Explanation
Correct Answer: A
There are a total of 5 + 3 = 8 balls in the bag. The probability of drawing a blue ball is the number of blue balls (3) divided by the total number of balls (8), which is 3/8 = 0.375.
Q3
Easy
If there are 4 different books and you want to choose 2 to take on a trip, in how many ways can you choose the books?
A.
12
B.
6
C.
8
D.
4
Show Answer & Explanation
Correct Answer: B
The number of ways to choose 2 books from 4 can be calculated using the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of books, and k is the number of books to choose. Here, C(4, 2) = 4! / (2!(4-2)!) = 6.
Q4
Medium
In a class of 30 students, 18 students play cricket, 12 students play soccer, and 6 students play both sports. How many students play neither cricket nor soccer?
A.
6
B.
12
C.
18
D.
24
Show Answer & Explanation
Correct Answer: A
Using the principle of inclusion-exclusion, the total number of students who play at least one sport is 18 + 12 - 6 = 24. Therefore, the number of students who play neither sport is 30 - 24 = 6.
Q5
Medium
A box contains 5 red balls, 3 blue balls, and 2 green balls. If one ball is drawn at random, what is the probability that it is blue?
A.
1/10
B.
3/10
C.
1/5
D.
1/3
Show Answer & Explanation
Correct Answer: B
The total number of balls is 5 + 3 + 2 = 10. The probability of drawing a blue ball is the number of blue balls divided by the total number of balls: 3/10.
Q6
Medium
If a six-sided die is rolled, what is the probability of rolling a number greater than 4?
A.
1/3
B.
1/6
C.
1/2
D.
1/4
Show Answer & Explanation
Correct Answer: A
The numbers greater than 4 on a six-sided die are 5 and 6, which are 2 outcomes. Therefore, the probability is 2 successful outcomes out of 6 total outcomes: 2/6 = 1/3.
Q7
Medium
A committee of 4 members is to be formed from 8 candidates. How many different committees can be formed?
A.
70
B.
80
C.
90
D.
100
Show Answer & Explanation
Correct Answer: A
The number of ways to choose 4 members from 8 candidates is calculated using the combination formula: C(n, r) = n! / [r!(n-r)!]. Thus, C(8, 4) = 70.
Q8
Hard
In a class of 30 students, 12 are boys and 18 are girls. If a student is chosen at random, what is the probability that the chosen student is either a boy or a girl with brown hair, given that 5 boys and 7 girls have brown hair?
A.
0.6333
B.
0.7333
C.
0.8667
D.
0.9333
Show Answer & Explanation
Correct Answer: B
The total number of students with brown hair is 5 boys + 7 girls = 12. Thus, the probability of picking a boy or a girl with brown hair is 12/30 = 0.7333.
Q9
Hard
A box contains 5 red, 7 green, and 3 blue balls. If two balls are drawn at random without replacement, what is the probability that both balls drawn are of the same color?
A.
0.25
B.
0.3
C.
0.2
D.
0.15
Show Answer & Explanation
Correct Answer: A
The total ways to choose 2 balls from 15 is 15C2 = 105. The ways to choose 2 red are 5C2 = 10, green are 7C2 = 21, and blue are 3C2 = 3. Total same color selections = 10 + 21 + 3 = 34. Thus, probability = 34/105 = 0.25.
Q10
Hard
In a class of 30 students, 18 play cricket, 15 play soccer, and 10 play both games. How many students play neither cricket nor soccer?
A.
7
B.
10
C.
12
D.
15
Show Answer & Explanation
Correct Answer: A
Using the principle of inclusion-exclusion: Total playing at least one game = (Cricket + Soccer - Both) = 18 + 15 - 10 = 23. Therefore, students playing neither = Total students - Those playing at least one = 30 - 23 = 7.
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Counting and Probability — Matric (South Africa) Matric Mathematics Practice Questions Online
This page contains 143 practice MCQs for the chapter Counting and Probability in Matric (South Africa) Matric Mathematics. The questions are organized by difficulty — 44 easy, 79 medium, 20 hard — so you can choose the right level for your preparation.
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