Probability Practice Questions
GCSE · GCSE Mathematics · 145 free MCQs with instant results and detailed explanations.
145
Total
57
Easy
67
Medium
21
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
A bag contains 3 red balls and 2 blue balls. If a ball is drawn at random, what is the probability that it is red?
A.
3/5
B.
2/5
C.
1/5
D.
1/2
Show Answer & Explanation
Correct Answer: A
The probability of drawing a red ball is the number of red balls divided by the total number of balls. There are 3 red balls and 2 blue balls, so the total is 5. Thus, the probability is 3/5.
Q2
Easy
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.
2/3
Show Answer & Explanation
Correct Answer: A
The numbers greater than 4 on a die are 5 and 6, giving us 2 favorable outcomes. There are 6 possible outcomes in total, so the probability is 2/6, which simplifies to 1/3.
Q3
Easy
A box contains 4 green, 3 yellow, and 1 blue marble. If a marble is picked at random, what is the probability of picking a yellow marble?
A.
1/4
B.
3/8
C.
1/2
D.
3/4
Show Answer & Explanation
Correct Answer: B
The probability of picking a yellow marble is the number of yellow marbles divided by the total number of marbles. There are 3 yellow marbles and a total of 8 marbles, so the probability is 3/8.
Q4
Medium
A box contains 5 red, 3 blue, and 2 green marbles. If one marble is drawn at random, what is the probability that it is blue?
A.
1/5
B.
1/4
C.
3/10
D.
1/3
Show Answer & Explanation
Correct Answer: C
The probability of drawing a blue marble is the number of blue marbles divided by the total number of marbles. There are 3 blue marbles and a total of 10 marbles, so the probability is 3/10.
Q5
Medium
A bag contains 4 black balls and 6 white balls. If two balls are drawn at random without replacement, what is the probability that both balls are black?
A.
2/15
B.
1/15
C.
4/15
D.
1/5
Show Answer & Explanation
Correct Answer: A
The probability of both balls being black is calculated by multiplying the probability of drawing the first black ball and the second black ball after the first has been drawn. The calculation is (4/10) * (3/9) = 12/90 = 2/15.
Q6
Medium
A student has a probability of 0.7 of passing a mathematics exam. What is the probability that they will fail the exam?
A.
0.3
B.
0.7
C.
0.5
D.
1.0
Show Answer & Explanation
Correct Answer: A
The probability of failing is the complement of passing. If the probability of passing is 0.7, then the probability of failing is 1 - 0.7 = 0.3.
Q7
Medium
In a class of 30 students, 18 are girls and 12 are boys. What is the probability of randomly selecting a boy?
A.
2/5
B.
1/3
C.
1/2
D.
3/5
Show Answer & Explanation
Correct Answer: A
The probability of selecting a boy is the number of boys divided by the total number of students. There are 12 boys and a total of 30 students, so the probability is 12/30, which simplifies to 2/5.
Q8
Hard
A bag contains 5 red, 3 blue, and 2 green marbles. If two marbles are drawn at random without replacement, what is the probability that both marbles are of the same color?
A.
0.24
B.
0.35
C.
0.20
D.
0.30
Show Answer & Explanation
Correct Answer: A
The probability of drawing two marbles of the same color can be calculated by finding the probabilities of drawing two red, two blue, and two green marbles separately, then summing these probabilities. The total favorable outcomes are 10 (10 ways to choose 2 marbles of the same color), and the total outcomes for drawing 2 from 10 marbles is 45. Thus, the probability is 10/45 = 0.24.
Q9
Hard
In a certain game, the probability of winning is 0.4. If a player plays the game 5 times, what is the probability that they win exactly 3 times?
A.
0.263
B.
0.200
C.
0.312
D.
0.160
Show Answer & Explanation
Correct Answer: A
The probability of winning exactly 3 times out of 5 can be calculated using the binomial probability formula: P(X=k) = C(n,k) * p^k * (1-p)^(n-k). Here, n=5, k=3, and p=0.4. Thus, the probability is C(5,3) * (0.4)^3 * (0.6)^2 = 10 * 0.064 * 0.36 = 0.263.
Q10
Hard
A bag contains 5 red, 3 blue, and 2 green marbles. If one marble is drawn at random, what is the probability that it is either red or blue?
A.
0.4
B.
0.5
C.
0.8
D.
0.6
Show Answer & Explanation
Correct Answer: C
The total number of marbles is 5 + 3 + 2 = 10. The number of favorable outcomes (red or blue) is 5 + 3 = 8. Therefore, the probability is 8/10 = 0.8.
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Probability — GCSE GCSE Mathematics Practice Questions Online
This page contains 145 practice MCQs for the chapter Probability in GCSE GCSE Mathematics. The questions are organized by difficulty — 57 easy, 67 medium, 21 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.