IB Maths AA SL · Unit 4: Statistics and Probability
Exam-style IB Maths AA 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.
P(A ∪ B) = P(A) + P(B) - P(A ∩ B). Independence means P(A ∩ B) = P(A)·P(B). SL AA Paper 1 questions almost always require the Venn diagram method. Probability — Venn diagrams and independence overview →
The question bank covers these probability question types (number of questions in brackets):
Independent events with $P(A) = 0.3$, $P(B) = 0.8$. Find $P(A \cap B)$ and $P(A \cup B)$.
1. Independence: $P(A \cap B) = 0.3 \times 0.8 = \mathbf{0.24}$.
2. Addition rule: $P(A \cup B) = 0.3 + 0.8 - 0.24 = \mathbf{0.86}$.
Bag has 4 red and 5 blue marbles. Two marbles drawn one after the other without replacement. Find the probability that they are different colours.
1. Two paths: (R then B) OR (B then R).
2. Path 1: $\frac{4}{9} \times \frac{5}{8} = \frac{20}{72}$.
3. Path 2: $\frac{5}{9} \times \frac{4}{8} = \frac{20}{72}$.
4. Sum: $\frac{40}{72} = \mathbf{\frac{5}{9}}$.
$P(D) = 0.02$, $P(\text{positive} \mid D) = 0.95$, $P(\text{positive} \mid D') = 0.10$. Given a positive test, find $P(D)$ (posterior).
1. Priors: $P(D) = 0.02$, $P(D') = 0.98$.
2. Total probability of positive: $P(P) = (0.02)(0.95) + (0.98)(0.10) = 0.019 + 0.098 = 0.117$.
3. Bayes: $P(D \mid P) = \frac{P(D \cap P)}{P(P)} = \frac{0.019}{0.117} = 0.16239\ldots \implies \mathbf{0.162}$.
Three questions from the bank, easiest first. Mark schemes and AI marking of your written working are in the practice area.
A biased coin has a probability of landing on tails of \(0.38\). The coin is tossed exactly \(250\) times.
Find the probability that the coin lands on heads on any single toss.
Calculate the expected number of times the coin will land on tails.
Calculate the expected number of times the coin will land on heads.
Two events \(C\) and \(D\) are such that \(P(C) = 0.55\) and \(P(D) = 0.4\). The probability of neither event occurring is \(P(C' \cap D') = 0.27\).
Find \(P(C \cup D)\).
Find \(P(C \cap D)\).
Find the probability that event \(C\) occurs, but event \(D\) does not.
A box contains \(n\) green apples and \(4\) red apples. Two apples are selected at random without replacement. The probability that both apples are green is exactly \(\frac{1}{3}\).
Formulate an algebraic equation in terms of \(n\) for the probability of selecting two green apples.
Use your graphic display calculator to solve the equation and find the exact number of green apples initially in the box.
There are 45 exam-style probability questions in the AA SL question bank (Paper 1: 32 · Paper 2: 13), graded 5 easy, 22 medium, 9 hard, 3 very hard, 6 starter. Every question has a full IB-style mark scheme (M, A and R marks).
Both. In the bank, Paper 1: 32 · Paper 2: 13. Paper 1 is non-calculator, so practise the exact-value algebra as well as the GDC methods.
Open the AA 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.