About Probability (Theoretical) — Class 8 IB

Calculate theoretical probability using sample spaces, tree diagrams, and organized lists. This topic is part of the IB Class 8 mathematics syllabus (chapter: Unit 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 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Probability (Theoretical) — solved examples for Class 8 IB

Practice questions on Probability (Theoretical)

1. Q1.easy

   A die is rolled. What is P(getting a 3)?

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

   Answer: \(\frac{1}{6}\)

   Hint: 6 equally likely outcomes.

2. Q2.easy

   An event that is certain has probability:

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

   Answer: 1

   Hint: Certain = guaranteed.

3. Q3.easy

   An impossible event has probability:

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

   Answer: 0

   Hint: Can never happen.

4. Q4.medium

   P(sum of 7 with two dice) = ?

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

   Answer: \(\frac{1}{6}\)

   Hint: Count: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1).

5. Q5.medium

   P(sum of 2 with two dice) = ?

   1. A)\(\frac{1}{36}\)
   2. B)\(\frac{1}{18}\)
   3. C)\(\frac{1}{12}\)
   4. D)\(\frac{1}{6}\)
   Show answer

   Answer: \(\frac{1}{36}\)

   Hint: Only (1,1).

6. Q6.medium

   A coin is flipped 3 times. P(all heads)?

   1. A)\(\frac{1}{2}\)
   2. B)\(\frac{1}{4}\)
   3. C)\(\frac{1}{6}\)
   4. D)\(\frac{1}{8}\)
   Show answer

   Answer: \(\frac{1}{8}\)

   Hint: Sample space has 2³ = 8 outcomes.

7. Q7.hard

   Two dice rolled. P(both show same number) = ?

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

   Answer: \(\frac{1}{6}\)

   Hint: Doubles: (1,1), (2,2), ..., (6,6).

8. Q8.hard

   A bag has 5 red and 3 blue balls. Two drawn WITHOUT replacement. P(both red) = ?

   1. A)\(\frac{25}{64}\)
   2. B)\(\frac{5}{14}\)
   3. C)\(\frac{20}{56}\)
   4. D)Both B and C
   Show answer

   Answer: Both B and C

   Hint: Without replacement changes the second probability.

9. Q9.hard

   P(A) = 0.4, P(B) = 0.5, P(A and B) = 0.2. Find P(A or B).

   1. A)0.7
   2. B)0.9
   3. C)0.1
   4. D)0.3
   Show answer

   Answer: 0.7

   Hint: P(A or B) = P(A) + P(B) - P(A and B).

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