About Probability — Class 10 ICSE

Apply probability rules to compound events, conditional probability basics, and tree diagrams. This topic is part of the ICSE Class 10 mathematics syllabus (chapter: Chapter 9). 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 10-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Probability — solved examples for Class 10 ICSE

Practice questions on Probability

1. Q1.easy

   A fair die is rolled. What is the probability of getting a number greater than $4$?

   1. A)$\frac{1}{6}$
   2. B)$\frac{1}{3}$
   3. C)$\frac{2}{3}$
   4. D)$\frac{1}{2}$
   Show answer

   Answer: $\frac{1}{3}$

   Hint: Numbers greater than 4 on a die are 5 and 6.

2. Q2.easy

   The probability of an impossible event is:

   1. A)$0$
   2. B)$1$
   3. C)$\frac{1}{2}$
   4. D)$-1$
   Show answer

   Answer: $0$

   Hint: An impossible event can never happen.

3. Q3.easy

   A card is drawn at random from a well-shuffled deck of $52$ cards. The probability of getting a king is:

   1. A)$\frac{1}{52}$
   2. B)$\frac{1}{13}$
   3. C)$\frac{1}{4}$
   4. D)$\frac{4}{13}$
   Show answer

   Answer: $\frac{1}{13}$

   Hint: There are 4 kings in a deck of 52 cards.

4. Q4.medium

   Two dice are thrown. What is the probability that the sum is at least $10$?

   1. A)$\frac{1}{12}$
   2. B)$\frac{1}{6}$
   3. C)$\frac{5}{36}$
   4. D)$\frac{7}{36}$
   Show answer

   Answer: $\frac{1}{6}$

   Hint: Sum >= 10 means sum is 10, 11, or 12. Count all pairs.

5. Q5.medium

   A bag contains $5$ red, $4$ green, and $3$ yellow balls. Two balls are drawn one after the other without replacement. What is the probability that both are red?

   1. A)$\frac{5}{33}$
   2. B)$\frac{25}{144}$
   3. C)$\frac{5}{12}$
   4. D)$\frac{10}{66}$
   Show answer

   Answer: $\frac{5}{33}$

   Hint: Without replacement: P(1st red) x P(2nd red | 1st was red).

6. Q6.medium

   A number is selected at random from $\{1, 2, 3, \ldots, 20\}$. What is the probability that it is a multiple of $3$ or $5$?

   1. A)$\frac{9}{20}$
   2. B)$\frac{7}{20}$
   3. C)$\frac{2}{5}$
   4. D)$\frac{11}{20}$
   Show answer

   Answer: $\frac{9}{20}$

   Hint: Multiples of 3: {3,6,9,12,15,18}. Multiples of 5: {5,10,15,20}. Watch for overlap at 15.

7. Q7.hard

   Three cards are drawn from a deck of $52$ cards without replacement. What is the probability that all three are kings?

   1. A)$\frac{1}{5525}$
   2. B)$\frac{1}{2197}$
   3. C)$\frac{4}{2197}$
   4. D)$\frac{1}{13000}$
   Show answer

   Answer: $\frac{1}{5525}$

   Hint: P = (4/52) × (3/51) × (2/50).

8. Q8.hard

   A bag has $4$ red, $3$ blue, and $2$ green balls. Three balls are drawn without replacement. What is the probability of getting one ball of each colour?

   1. A)$\frac{2}{7}$
   2. B)$\frac{24}{84}$
   3. C)$\frac{2}{9}$
   4. D)$\frac{4}{21}$
   Show answer

   Answer: $\frac{2}{7}$

   Hint: Use combinations: C(4,1) × C(3,1) × C(2,1) / C(9,3).

9. Q9.hard

   Two dice are thrown. What is the probability that the product of the two numbers is a perfect square?

   1. A)$\frac{8}{36}$
   2. B)$\frac{10}{36}$
   3. C)$\frac{7}{36}$
   4. D)$\frac{9}{36}$
   Show answer

   Answer: $\frac{8}{36}$

   Hint: List all pairs (a,b) where a×b is a perfect square (1, 4, 9, 16, 25, 36).

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.