Free Probability questions for IB Mathematics: Analysis & Approaches (SL & HL), part of Statistics & probability. Each question has the answer and the marking points an examiner would look for.
Generate a full Probability worksheet →All Statistics & probability questionsEvents A and B are independent, with P(B) = 0.4 and P(A ∪ B) = 0.76.
Find P(A).
Find P(A | B′).
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 0.6 P(A ∪ B) = P(A) + P(B) − P(A)P(B) M1 x + 0.4 − 0.4x = 0.76 A1 0.6x = 0.36 (A1) P(A) = 0.6 A1 | 4 |
| (b) | 0.6 independence of A and B′ R1 0.6 A1 | 2 |
A bag contains 5 red balls and 4 green balls. Two balls are taken at random from the bag, without replacement.
Find the probability that both balls are the same colour.
Given that both balls are the same colour, find the probability that they are both red.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 49 59 × 48 + 49 × 38 (M1)(A1) 49 A1 | 3 |
| (b) | 58 P(RR)P(same) (M1) 5/184/9 (A1) 58 A1 | 3 |
Events A and B are such that P(A) = 0.5, P(B) = 0.5 and P(A ∪ B) = 0.81.
Find P(A ∩ B).
Find P(A | B).
Determine whether A and B are independent. Justify your answer.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 0.19 0.5 + 0.5 − P(A ∩ B) = 0.81 (M1) 0.19 A1 | 2 |
| (b) | 0.38 0.190.5 (M1) 0.38 A1 | 2 |
| (c) | not independent P(A)P(B) = 0.25 ≠ P(A ∩ B) R1 not independent A1 | 2 |
A bag contains 3 red and 2 blue marbles. Two marbles are taken without replacement.
Find the probability that both are red.
Given that at least one marble is red, find the probability that both are red.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 310 35 × 24 (M1) 310 A1 | 2 |
| (b) | 13 P(at least one red) = 1 − P(both blue) (M1) conditional probability formula (M1) 13 A1 | 3 |
Events A and B are independent, with P(B) = 0.5 and P(A ∪ B) = 0.8.
Find P(A).
Find P(A | B′).
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 0.6 P(A ∪ B) = P(A) + P(B) − P(A)P(B) M1 x + 0.5 − 0.5x = 0.8 A1 0.5x = 0.3 (A1) P(A) = 0.6 A1 | 4 |
| (b) | 0.6 independence of A and B′ R1 0.6 A1 | 2 |
A bag contains 7 red balls and 2 green balls. Two balls are taken at random from the bag, without replacement.
Find the probability that both balls are the same colour.
Given that both balls are the same colour, find the probability that they are both red.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 1118 79 × 68 + 29 × 18 (M1)(A1) 1118 A1 | 3 |
| (b) | 2122 P(RR)P(same) (M1) 7/1211/18 (A1) 2122 A1 | 3 |
Riyaz Shaikh has mentored IGCSE, IB and A Level students for 15+ years, one-on-one, online and in Mumbai. The hardest questions on this site are the ones he uses to find a student's weak points.
Meet Riyaz →Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in