IB Maths AA SL · Unit 4: Statistics and Probability
IB Maths AA SL Discrete Random Variables Questions
Exam-style IB Maths AA SL discrete random variables 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.
- 33 questions
- Paper 1: 19
- Paper 2: 14
- 8 easy
- 12 medium
- 6 hard
- 3 very hard
- 4 starter
- 3 worked examples
Practise Discrete Random Variables questions →
AA SL formula booklet
What's examined in AA SL discrete random variables
The question bank covers these discrete random variables question types (number of questions in brackets):
- Discrete Prob. Distributions (17)
- Binomial Probabilities (10)
- Binomial Parameters (6)
Key formulas
- Expected value (discrete)
- \(E(X) = \sum x P(X=x)\)
- Mean & variance of a binomial
- \(E(X) = np,\quad \mathrm{Var}(X) = np(1-p)\)
- Standardising a normal variable
- \(Z = \dfrac{X - \mu}{\sigma}\)
In the same notation as the IB formula booklet. All AA SL formulas →
Discrete Random Variables worked examples
Worked example 1: Finding probability constants and expected value · easy
A biased 4-sided die has $P(X=1) = P(X=2) = P(X=3) = p$ and $P(X=4) = \frac{1}{2}$. Find $p$ and $E(X)$.
1. Sum of probabilities $= 1$: $3p + \frac{1}{2} = 1$.
2. Solve: $p = \mathbf{\frac{1}{6}}$.
3. Expected value: $E(X) = 1(\tfrac{1}{6}) + 2(\tfrac{1}{6}) + 3(\tfrac{1}{6}) + 4(\tfrac{3}{6}) = \frac{1+2+3+12}{6} = \mathbf{3}$.
Examiner tip: Multiply each outcome by its probability BEFORE adding. Averaging the outcomes alone is a common mistake.
Worked example 2: Solving for a missing prize in a fair game · medium
A game costs $\text{€}3$. Prize distribution: $P(W=0)=0.4, P(W=2)=0.3, P(W=5)=0.2, P(W=A)=0.1$. Given the game is fair, find $A$.
1. Fair game: $E(W) = 3$ (cost of play).
2. Set up: $0(0.4) + 2(0.3) + 5(0.2) + A(0.1) = 3$.
3. Simplify: $1.6 + 0.1A = 3$.
4. Solve: $0.1A = 1.4 \implies \mathbf{A = 14}$.
Examiner tip: A "fair game" makes expected NET gain zero, which is equivalent to $E(\text{payout}) = \text{cost}$.
Worked example 3: Conditional binomial probability · hard
Defect rate $12\%$, sample $n=50$. Given the inspector finds fewer than 8 defective chips, find $P(D = 5 \mid D < 8)$.
1. Distribution: $D \sim B(50, 0.12)$.
2. Formula: $P(D = 5 \mid D < 8) = \frac{P(D = 5)}{P(D \le 7)}$ (since $\{D=5\} \subset \{D \le 7\}$).
3. Numerator (Binomial PD): $P(D = 5) = 0.16378\ldots$
4. Denominator (Binomial CD, $0 \le D \le 7$): $P(D \le 7) = 0.75548\ldots$
5. Divide: $\frac{0.16378\ldots}{0.75548\ldots} = \mathbf{0.217}$.
Examiner tip: "Fewer than 8" for a discrete variable is $\le 7$, NOT $\le 8$.
Try these IB Maths AA SL discrete random variables 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 2
A fair coin is tossed 20 times and the number of times it lands heads up is recorded as the random variable \(X\).
Find the expected number of times that the coin will land heads up.
Use your graphic display calculator to find the probability that the coin lands heads up exactly 15 times.
Question 2 · medium · 5 marks · Paper 1
The probability distribution of a discrete random variable \(X\) is given by the formula:
\[P(X = x) = \frac{x}{k} \quad \text{for } x \in \{1, 2, 3, 4\}\]
where \(k\) is a positive constant.
Find the exact value of \(k\).
Find the expected value, \(E(X)\).
Question 3 · hard · 5 marks · Paper 2
A company manufactures computer chips. It is known that \(12\%\) of the chips produced are defective. A quality control inspector takes a random sample of 50 chips.
Let the random variable \(D\) represent the number of defective chips in the sample.
Find the probability that the inspector finds fewer than 8 defective chips.
Given that the inspector finds fewer than 8 defective chips, find the conditional probability that they found exactly 5 defective chips.
All 33 discrete random variables questions with mark schemes →
FAQ
How many IB Maths AA SL discrete random variables questions are there?
There are 33 exam-style discrete random variables questions in the AA SL question bank (Paper 1: 19 · Paper 2: 14), graded 8 easy, 12 medium, 6 hard, 3 very hard, 4 starter. Every question has a full IB-style mark scheme (M, A and R marks).
Is discrete random variables on Paper 1 or Paper 2?
Both. In the bank, Paper 1: 19 · Paper 2: 14. Paper 1 is non-calculator, so practise the exact-value algebra as well as the GDC methods.
Where can I get the mark schemes?
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.
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