Probability Practice Questions
KCSE (Kenya) · KCSE Mathematics · 141 free MCQs with instant results and detailed explanations.
141
Total
44
Easy
73
Medium
24
Hard
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Sample Questions from Probability
Here are 10 sample questions. Start a quiz to get randomized questions with scoring.
Q1
Easy
In a class, 4 students are wearing glasses and 6 are not. If one student is selected at random, what is the probability that the student is wearing glasses?
A.
2/5
B.
1/3
C.
4/10
D.
4/6
Show Answer & Explanation
Correct Answer: C
The probability of selecting a student wearing glasses is the number of students wearing glasses divided by the total number of students. There are 4 students wearing glasses out of 10 total students, giving a probability of 4/10, which simplifies to 2/5.
Q2
Easy
A die is rolled once. What is the probability of rolling an even number?
A.
1/2
B.
1/3
C.
2/3
D.
1/6
Show Answer & Explanation
Correct Answer: A
An even number on a die can be 2, 4, or 6. There are 3 even numbers out of a total of 6 possible outcomes when rolling a die. Therefore, the probability of rolling an even number is 3/6, which simplifies to 1/2.
Q3
Easy
A bag contains 3 red balls and 2 blue balls. If one ball is drawn at random, what is the probability that it is blue?
A.
2/5
B.
1/2
C.
1/5
D.
3/5
Show Answer & Explanation
Correct Answer: A
The total number of balls is 3 red + 2 blue = 5. The probability of drawing a blue ball is the number of blue balls divided by the total number of balls, which is 2/5.
Q4
Medium
A box contains 8 red balls and 12 blue balls. If a ball is randomly drawn from the box, what is the probability that it is blue?
A.
0.4
B.
0.6
C.
0.5
D.
0.2
Show Answer & Explanation
Correct Answer: B
The total number of balls is 8 + 12 = 20. The probability of drawing a blue ball is the number of blue balls divided by the total number of balls, which is 12/20 = 0.6.
Q5
Medium
In a class of 30 students, 18 students prefer Mathematics, 12 prefer Physics, and 6 prefer both subjects. What is the probability that a student selected at random prefers either Mathematics or Physics?
A.
0.6
B.
0.8
C.
0.5
D.
0.4
Show Answer & Explanation
Correct Answer: B
Using the principle of inclusion-exclusion, the number of students who prefer either subject is 18 + 12 - 6 = 24. The probability is 24/30 = 0.8.
Q6
Medium
A jar contains 5 green, 3 yellow, and 2 black marbles. If one marble is drawn at random, what is the probability that it is not green?
A.
0.4
B.
0.5
C.
0.6
D.
0.3
Show Answer & Explanation
Correct Answer: C
The total number of marbles is 5 + 3 + 2 = 10. The number of non-green marbles (yellow + black) is 3 + 2 = 5. Thus, the probability of not drawing a green marble is 5/10 = 0.6.
Q7
Medium
If two cards are drawn from a standard deck of 52 cards without replacement, what is the probability that both are hearts?
A.
1/26
B.
1/17
C.
1/52
D.
1/221
Show Answer & Explanation
Correct Answer: D
The probability of the first card being a heart is 13/52. If the first card is a heart, there are now 12 hearts left from 51 total cards. So, the probability of drawing two hearts is (13/52) * (12/51) = 1/221.
Q8
Hard
A bag contains 8 red, 6 blue, and 4 green balls. If three balls are drawn at random, what is the probability that at least one of them is red?
A.
0.75
B.
0.68
C.
0.80
D.
0.82
Show Answer & Explanation
Correct Answer: A
The probability that at least one ball is red can be found by calculating the complement of the event that no balls drawn are red. The total number of balls is 18. The probability of drawing no red balls (only blue and green) is (10/18) * (9/17) * (8/16). Thus, the probability of at least one red is 1 - (10/18) * (9/17) * (8/16) = 0.75.
Q9
Hard
A box contains 4 red balls, 6 blue balls, and 10 green balls. If two balls are drawn at random without replacement, what is the probability that both balls are of different colors?
A.
0.76
B.
0.68
C.
0.74
D.
0.60
Show Answer & Explanation
Correct Answer: A
To find the probability that both drawn balls are of different colors, first calculate the total number of ways to choose 2 balls from 20 (the total number of balls). Then, find the combinations where both balls are of the same color and subtract from the total. Finally, use this to calculate the probability of drawing different colored balls, which results in approximately 0.76.
Q10
Hard
A box contains 5 red balls, 3 blue balls, and 2 green balls. If two balls are drawn at random without replacement, what is the probability that both balls are of different colors?
A.
0.7
B.
0.6
C.
0.5
D.
0.8
Show Answer & Explanation
Correct Answer: A
To find the probability that both balls drawn are of different colors, we first calculate the total number of ways to choose 2 balls from 10. Then, we determine the ways to choose 2 balls of the same color and subtract this from the total combinations, leading to a probability of 0.7.
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Probability — KCSE (Kenya) KCSE Mathematics Practice Questions Online
This page contains 141 practice MCQs for the chapter Probability in KCSE (Kenya) KCSE Mathematics. The questions are organized by difficulty — 44 easy, 73 medium, 24 hard — so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.