How many practice questions are available for Probability?

SparkEd Math offers 60+ practice questions for Probability across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Probability content free on SparkEd Math?

Yes! All Probability content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Probability differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Probability problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Probability content aligned with the ICSE syllabus?

Yes, all Probability questions and lessons on SparkEd Math are fully aligned with the Indian Certificate of Secondary Education (ICSE) syllabus for Class 9. The content follows the official curriculum structure and exam pattern.

Probability — Class 9 ICSE (2025-26)

About Probability — Class 9 ICSE

Compute probability of events using sample spaces and apply addition rule. This topic is part of the ICSE Class 9 mathematics syllabus (chapter: Chapter 14). On this page you can practice 59 questions across three difficulty levels — 20 easy, 19 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 34-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Probability

Introduction to Probability: Understanding Randomness
Calculating Probability: The Fundamental Formula
Probability with Standard Cards and Dice
The Addition Rule for Mutually Exclusive Events
Recap and Exam Readiness

Interactive lesson · about 15 minutes · checkpoint question after every unit

Probability — solved examples for Class 9 ICSE

Example 1easy

Which of the following statements about the probability of an event E is always true?

A)P(E) > 1
B)P(E) < 0
C)0 ≤ P(E) ≤ 1
D)P(E) = 1.5

Step-by-step solution

The probability of any event E, denoted as P(E), represents the likelihood of that event occurring.
By definition, the number of favourable outcomes n(E) cannot be negative and cannot exceed the total number of outcomes n(S).
Therefore, 0 ≤ n(E) ≤ n(S).
Dividing by n(S), we get 0/n(S) ≤ n(E)/n(S) ≤ n(S)/n(S), which simplifies to 0 ≤ P(E) ≤ 1.

Answer: 0 ≤ P(E) ≤ 1

Example 2medium

A fair six-sided die is rolled once. What is the probability of getting an even number?

A)1/6
B)1/3
C)1/2
D)2/3

Step-by-step solution

The sample space when rolling a fair six-sided die is S = {1, 2, 3, 4, 5, 6}. So, the total number of possible outcomes is 6.
Let E be the event of getting an even number. The favorable outcomes are E = {2, 4, 6}. The number of favorable outcomes is 3.
The probability of an event E is P(E) = (Number of favorable outcomes) / (Total number of possible outcomes).
$P(E) = 3 / 6 = 1/2$

Answer: 1/2

Example 3hard

Three distinct fair dice are rolled simultaneously. What is the probability that the sum of the numbers appearing on the dice is exactly 16?

A)1/36
B)5/216
C)7/216
D)1/72

Step-by-step solution

The total number of outcomes when three distinct fair dice are rolled is 6 × 6 × 6 = 216.
The favorable outcomes where the sum of the numbers is 16 are (listing permutations):
$(4, 6, 6), (6, 4, 6), (6, 6, 4) -> 3 outcomes (5, 5, 6), (5, 6, 5), (6, 5, 5) -> 3 outcomes$
So, there are 3 + 3 = 6 favorable outcomes.
The probability is the ratio of favorable outcomes to the total number of outcomes.
$P(Sum=16) = 6 / 216 = 1/36$

Answer: 1/36

Practice questions on Probability

Q1.easy
A fair six-sided die is rolled, and a fair coin is tossed simultaneously. Which of the following correctly represents the sample space (S) for this experiment?
1. A)S = {1, 2, 3, 4, 5, 6, Head, Tail}
2. B)S = {(1,H), (2,H), (3,H), (4,H), (5,H), (6,H), (1,T), (2,T), (3,T), (4,T), (5,T), (6,T)}
3. C)S = {H, T, 1, 2, 3, 4, 5, 6}
4. D)S = {(H,T), (1,2), (3,4), (5,6)}
Show answer
Answer: S = {(1,H), (2,H), (3,H), (4,H), (5,H), (6,H), (1,T), (2,T), (3,T), (4,T), (5,T), (6,T)}
Hint: When two independent events occur, the sample space consists of all possible combinations of their individual outcomes.
Q2.easy
A bag contains 5 red balls, 3 blue balls, and 2 green balls. If a ball is drawn at random from the bag, what is the probability that the ball drawn is blue?
1. A)1/5
2. B)3/10
3. C)1/2
4. D)2/5
Show answer
Answer: 3/10
Hint: First, find the total number of balls in the bag. Then, identify the number of blue balls.
Q3.easy
Rahul states that if the probability of an event happening is 'p', then the probability of the event not happening is '1-p'. Which of the following situations correctly demonstrates this concept?
1. A)If the probability of rain is 0.6, the probability of no rain is 0.4.
2. B)If the probability of drawing a red card from a deck is 1/2, the probability of drawing a black card is also 1/2.
3. C)If the probability of rolling an even number on a die is 1/2, the probability of rolling an odd number is 1/2.
4. D)All of the above.
Show answer
Answer: All of the above.
Hint: Consider what 'not happening' means for each scenario. Does it cover all other possibilities?
Q4.medium
Two unbiased coins are tossed simultaneously. What is the probability of getting exactly one head?
1. A)1/4
2. B)1/2
3. C)3/4
4. D)1
Show answer
Answer: 1/2
Hint: List all possible outcomes when tossing two coins. Then, identify the outcomes where exactly one head appears.
Q5.medium
A bag contains 5 red balls, 3 blue balls, and 2 green balls. If one ball is drawn at random from the bag, what is the probability that it is a blue ball?
1. A)3/10
2. B)1/5
3. C)1/2
4. D)3/5
Show answer
Answer: 3/10
Hint: First, find the total number of balls in the bag. Then, determine how many of them are blue.
Q6.medium
Which of the following values cannot be the probability of an event?
1. A)0.7
2. B)1/3
3. C)-0.5
4. D)0
Show answer
Answer: -0.5
Hint: Remember the fundamental property of probability: its value must always fall within a specific range.
Q7.hard
From a well-shuffled deck of 52 playing cards, three cards are drawn one after the other without replacement. What is the probability that the first card drawn is a King, the second is a Queen, and the third is an Ace?
1. A)4/5525
2. B)8/16575
3. C)16/140608
4. D)64/132600
Show answer
Answer: 8/16575
Hint: Calculate the probability of drawing each card sequentially, remembering that the total number of cards and the number of specific cards decrease after each draw.
Q8.hard
A survey of 300 students in a school revealed that 150 students like Mathematics, 90 students like Science, and 30 students like both subjects. If a student is chosen randomly from the school, what is the probability that the student likes exactly one of the two subjects?
1. A)2/5
2. B)3/5
3. C)11/15
4. D)1/3
Show answer
Answer: 3/5
Hint: Use a Venn diagram approach to find the number of students who like only Math and only Science. Then, sum these numbers to get the total who like exactly one subject.
Q9.hard
Let E be an event and E' be its complementary event. Which of the following statements must ALWAYS be true?
1. A)P(E) × P(E') = 1
2. B)P(E) > P(E')
3. C)0 ≤ P(E) ≤ 1
4. D)P(E) - P(E') = 0.5
Show answer
Answer: 0 ≤ P(E) ≤ 1
Hint: Recall the fundamental axioms of probability that define the possible range of any event's probability.

These are 9 of the 59 questions available for Probability. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.