IB Maths AI SL · Unit 4: Statistics and Probability
IB Maths AI SL Probability Questions
Exam-style IB Maths AI SL probability questions with worked solutions. Start with the 3 fully worked examples below — each is solved step by step the way an IB examiner expects — then try the practice questions and check your working against the mark scheme.
- 42 questions
- Paper 1: 23
- Paper 2: 19
- 3 easy
- 10 medium
- 14 hard
- 9 very hard
- 6 starter
- 3 worked examples
Practise Probability questions →
AI SL formula booklet
What's examined in AI SL probability
The question bank covers these probability question types (number of questions in brackets):
- Venn Diagrams & Set Formulas (23)
- Conditional & Compound Events (16)
- Sample Space Enumeration (3)
Key formulas
- Probability of an event
- \(P(A) = \dfrac{n(A)}{n(U)}\)
- Conditional probability
- \(P(A \mid B) = \dfrac{P(A \cap B)}{P(B)}\)
- Independent events
- \(P(A \cap B) = P(A)\,P(B)\)
- Complementary events
- \(P(A') = 1 - P(A)\)
- Combined events
- \(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)
- Mutually exclusive events
- \(P(A \cap B) = 0\)
In the same notation as the IB formula booklet. All AI SL formulas →
Probability worked examples
Worked example 1: Sample space and simple probability · easy
A fair coin and a fair 4-sided die (1–4) are rolled. Find the exact probability of a Head and a prime number.
1. Sample space (8 outcomes): $\{H1,H2,H3,H4,T1,T2,T3,T4\}$.
2. Primes on die: $2$ and $3$ ($1$ is not prime).
3. Favourable: $\{H2, H3\}$, so $2$ outcomes.
4. Fraction: $\frac{2}{8}$.
5. Simplify: $\mathbf{0.25}$ (or $\frac{1}{4}$).
Examiner tip: Listing the full sample space visually (grid/table) prevents missing overlapping outcomes under exam pressure.
Worked example 2: Tree diagram — exactly one of two days · medium
$P(\text{rain})=0.4$ each day, independent. Find the exact probability of rain on exactly one of two consecutive days.
1. Two paths: (Rain, No Rain) or (No Rain, Rain).
2. $P(\text{no rain})$: $1 - 0.4 = 0.6$.
3. Path 1: $0.4 \times 0.6 = 0.24$.
4. Path 2: $0.6 \times 0.4 = 0.24$.
5. Sum: $0.24 + 0.24 = \mathbf{0.48}$.
Examiner tip: "Exactly one day" can occur in two chronological orders — both must be added.
Worked example 3: Conditional probability without replacement · hard
Bag: $4$ red, $5$ green marbles. Two drawn without replacement. Given the second is green, find $P(\text{first is green})$.
1. Formula: $P(G_1 \mid G_2) = \frac{P(G_1 \cap G_2)}{P(G_2)}$.
2. $P(G_1 \cap G_2)$: $\frac{5}{9} \times \frac{4}{8} = \frac{20}{72}$.
3. $P(R_1 \cap G_2)$: $\frac{4}{9} \times \frac{5}{8} = \frac{20}{72}$.
4. $P(G_2)$: $\frac{20}{72} + \frac{20}{72} = \frac{40}{72}$.
5. Divide: $\frac{20/72}{40/72} = \mathbf{0.5}$ (or $\tfrac{1}{2}$).
Examiner tip: "Without replacement" — the denominator drops from 9 to 8, and the chosen colour's numerator drops by 1.
Try these IB Maths AI SL probability questions
Three questions from the bank, easiest first. Mark schemes and AI marking of your written working are in the practice area.
Question 1 · easy · 4 marks · Paper 1
Events A and B are mutually exclusive. It is given that \(P(A) = 0.25\) and \(P(B) = 0.35\).
Find \(P(A \cup B)\).
Find \(P(A' \cap B')\), the probability that neither event A nor event B occurs.
Question 2 · medium · 5 marks · Paper 1
Two fair 5-sided dice, each numbered 1 to 5, are rolled. The sum of the two numbers shown is recorded.
Find the probability that the sum of the two dice is strictly greater than 7.
Given that the sum of the two dice is strictly greater than 7, find the probability that the sum is exactly 9.
Question 3 · hard · 4 marks · Paper 1
Events A and B are mutually exclusive. It is known that \(P(A) = 2x\) and \(P(B) = x\). Given that \(P(A \cup B) = 0.9\), find the value of \(x\).
All 42 probability questions with mark schemes →
FAQ
How many IB Maths AI SL probability questions are there?
There are 42 exam-style probability questions in the AI SL question bank (Paper 1: 23 · Paper 2: 19), graded 3 easy, 10 medium, 14 hard, 9 very hard, 6 starter. Every question has a full IB-style mark scheme (M, A and R marks).
Is probability on Paper 1 or Paper 2?
Both. In the bank, Paper 1: 23 · Paper 2: 19. Practise with your GDC — AI papers expect calculator methods throughout.
Where can I get the mark schemes?
Open the AI SL Unit 4 practice page: every question has a step-by-step IB-style mark scheme, and you can photograph your working for instant AI marking. The worked examples on this page are free.
Probability in other IB Maths courses
← All IB Maths AI SL topics