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 Olympiad syllabus?

Yes, all Probability questions and lessons on SparkEd Math are fully aligned with the Mathematical Olympiad Preparation (Olympiad) syllabus for Class 10. The content follows the official curriculum structure and exam pattern.

Probability — Class 10 Olympiad (2025-26)

About Probability — Class 10 Olympiad

Compute theoretical probability, solve problems on complementary events, and tackle Olympiad-level probability puzzles. This topic is part of the Olympiad Class 10 mathematics syllabus (chapter: Module 12). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Probability — solved examples for Class 10 Olympiad

Example 1easy

From the first 100 positive integers, one number is chosen at random. What is the probability that the chosen number is divisible by 4 but not by 6?

A)17/100
B)1/5
C)1/4
D)13/100

Step-by-step solution

The total number of outcomes is 100 (integers from 1 to 100).
Numbers divisible by 4 in the range 1 to 100 are 4, 8, ..., 100. There are 100/4 = 25 such numbers.
Numbers divisible by 4 AND 6 are numbers divisible by their LCM, which is 12. Numbers divisible by 12 in this range are 12, 24, ..., 96. There are 100/12 = 8 such numbers (96/12 = 8).
Numbers divisible by 4 but NOT by 6 are the numbers divisible by 4 minus those also divisible by 12. So, 25 - 8 = 17. The probability is 17/100.

Answer: 17/100

Example 2medium

Numbers from 1 to 200 are written on individual slips of paper and placed in a box. A slip is drawn at random. What is the probability that the number on the slip is a multiple of 4 or 6, but not a multiple of 10?

A)13/50
B)17/100
C)27/100
D)31/200

Step-by-step solution

Total numbers = 200. Let M(n) denote the set of multiples of n.
Number of multiples of 4: N(M(4)) = floor(200/4) = 50.
Number of multiples of 6: N(M(6)) = floor(200/6) = 33.
Number of multiples of 12 (LCM of 4 and 6): N(M(12)) = floor(200/12) = 16.
Numbers that are multiples of 4 or 6: N(M(4) U M(6)) = N(M(4)) + N(M(6)) - N(M(12)) = 50 + 33 - 16 = 67.
Now, we need to exclude numbers that are also multiples of 10. These are multiples of LCM(4,10)=20 or LCM(6,10)=30. The overlap is LCM(4,6,10)=60. So, N((M(4) U M(6)) ∩ M(10)) = N(M(20)) + N(M(30)) - N(M(60)) = floor(200/20) + floor(200/30) - floor(200/60) = 10 + 6 - 3 = 13.
Favorable outcomes = 67 - 13 = 54.
Probability = 54/200 = 27/100.

Answer: 27/100

Example 3hard

A bag contains 5 red balls and 7 blue balls. If 4 balls are drawn at random without replacement, what is the probability that exactly 2 of them are red and at least one is blue?

A)35/99
B)70/99
C)14/33
D)42/99

Step-by-step solution

Total number of ways to draw 4 balls from 12 (5 red + 7 blue) is C(12, 4) = (12 × 11 × 10 × 9) / (4 × 3 × 2 × 1) = 495.
For exactly 2 red balls, the remaining 2 balls must be blue to make a total of 4. Ways to draw 2 red balls from 5 is C(5, 2) = 10.
Ways to draw 2 blue balls from 7 is C(7, 2) = 21. The condition 'at least one blue' is automatically satisfied.
Number of favorable outcomes = C(5, 2) × C(7, 2) = 10 × 21 = 210. The probability is 210/495, which simplifies to 14/33.

Answer: 14/33

Practice questions on Probability

Q1.easy
A box contains 5 red, 3 blue, and 2 green balls. If two balls are drawn at random without replacement, what is the probability that at least one of the balls drawn is red?
1. A)1/3
2. B)7/9
3. C)1/2
4. D)3/10
Show answer
Answer: 7/9
Hint: It's often easier to calculate the probability of the complementary event: 'neither ball drawn is red', and then subtract from 1.
Q2.easy
Two fair dice are rolled simultaneously. What is the probability that the product of the numbers shown on the dice is a perfect square?
1. A)1/6
2. B)1/9
3. C)2/9
4. D)5/36
Show answer
Answer: 2/9
Hint: List all possible pairs of outcomes and their products. Then identify which of these products are perfect squares.
Q3.easy
From a well-shuffled deck of 52 playing cards, one card is drawn at random. What is the probability that the card is either a King or a black card?
1. A)7/26
2. B)1/2
3. C)15/26
4. D)7/13
Show answer
Answer: 7/13
Hint: Remember the principle of inclusion-exclusion for 'OR' events: P(A or B) = P(A) + P(B) - P(A and B).
Q4.medium
A fair coin is tossed 4 times. What is the probability of getting at least one sequence of two consecutive heads (HH)?
1. A)7/16
2. B)9/16
3. C)11/16
4. D)13/16
Show answer
Answer: 9/16
Hint: Consider the complementary event: no sequence of two consecutive heads. List all outcomes for this and subtract from the total.
Q5.medium
Two fair dice are rolled simultaneously. What is the probability that the product of the numbers on the dice is a perfect square, given that the sum of the numbers is greater than 7?
1. A)1/5
2. B)1/6
3. C)1/3
4. D)2/15
Show answer
Answer: 1/5
Hint: First, identify the reduced sample space where the sum is greater than 7. Then, find the outcomes in this space where the product is a perfect square.
Q6.medium
From a standard deck of 52 playing cards, two cards are drawn one after the other without replacement. What is the probability that the first card is a King and the second card is a red card?
1. A)1/52
2. B)1/104
3. C)1/26
4. D)25/1326
Show answer
Answer: 1/26
Hint: Consider two cases for the first card: a red King or a black King. Calculate the probability for each case and sum them up.
Q7.hard
A point is chosen uniformly at random inside a square with vertices at (0,0), (1,0), (1,1), and (0,1). What is the probability that the sum of the coordinates of the point is less than 0.5?
1. A)1/8
2. B)1/16
3. C)1/4
4. D)1/2
Show answer
Answer: 1/8
Hint: The sample space is the area of the square. The favorable region is defined by the inequality x + y < 0.5 within the square.
Q8.hard
Three distinct numbers are chosen randomly from the set {1, 2, ..., 10}. What is the probability that at least one of the chosen numbers is a multiple of 3?
1. A)1/2
2. B)7/24
3. C)5/6
4. D)17/24
Show answer
Answer: 17/24
Hint: It's often easier to calculate the probability of the complementary event: none of the chosen numbers are multiples of 3.
Q9.hard
Two distinct numbers are chosen randomly from the set {1, 2, 3, ..., 15}. What is the probability that their sum is a prime number?
1. A)1/7
2. B)1/3
3. C)2/15
4. D)3/14
Show answer
Answer: 1/3
Hint: List all possible sums of two distinct numbers from the set. Then identify which of these sums are prime numbers.

These are 9 of the 60 questions available for Probability. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.