10 free IB Mathematics: Analysis & Approaches Statistics & Probability questions written in the style of IB Mathematics: Analysis & Approaches papers, each with its answer and mark scheme. 3 of them are A* challenge questions, built to catch the mistakes strong students still make.
This topic covers Descriptive statistics, Correlation & regression, Probability, Discrete random variables, Binomial distribution, Normal distribution, Bayes' theorem, Continuous random variables. Work through the questions below, then generate a full Statistics & Probability paper with a fresh set every time.
Generate a full Statistics & Probability paper →The data set {8, 2, 3, a, b} has mean 6 and variance 425, where a < b.
Find the values of a and b.
| Part | Answer and marking points | Marks |
|---|---|---|
| a = 8, b = 9 a + b = 17 A1 use of variance = Σx2n − x̄2 M1 a2 + b2 = 145 A1 substituting b = 17 − a M1 a2 − 17a + 72 = 0 A1 a = 8, b = 9 A1 | 6 |
A random variable X ~ B(n, p) has mean 9 and variance 3.6.
Find the value of p and the value of n.
Find P(X ≤ 8).
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | p = 0.6, n = 15 np = 9, np(1 − p) = 3.6 (M1) 1 − p = 0.4 A1 p = 0.6 A1 n = 15 A1 | 4 |
| (b) | 0.390 binomial CDF (M1) 0.390 A1 | 2 |
The probability that a component is faulty is 0.1. Find the least number of components that must be tested so that the probability of finding at least one faulty component is greater than 0.95.
| Part | Answer and marking points | Marks |
|---|---|---|
| 29 1 − (1 − 0.1)n > 0.95 (M1)(A1) solving (M1) 29 A1 | 4 |
For a set of test scores, the lower quartile is 24, the median is 28 and the upper quartile is 32. The smallest score is 17 and the largest score is 41.
Find the interquartile range.
Determine whether the largest score is an outlier. Justify your answer.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 8 8 A1 | 1 |
| (b) | not an outlier upper boundary Q3 + 1.5 × IQR (M1) = 44 A1 41 < 44, so it is not an outlier R1 | 3 |
A continuous random variable X has probability density function f(x) = kx2 for 0 ≤ x ≤ 4, and 0 otherwise.
Find k.
Find E(X).
Find the median of X.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 364 ∫ f(x) dx = 1 (M1) 364 A1 | 2 |
| (b) | 3 ∫ x f(x) dx (M1) 3 A1 | 2 |
| (c) | 3.17 ∫ from 0 to m = 0.5 (M1) m3 = 642 (A1) 3.17 A1 | 3 |
A bag contains 4 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) | 37 48 × 37 + 48 × 37 (M1)(A1) 37 A1 | 3 |
| (b) | 12 P(RR)P(same) (M1) 3/143/7 (A1) 12 A1 | 3 |
Machines A, B and C produce 40%, 35% and 25% of the items made in a factory. The percentages of defective items they produce are 2%, 3% and 5% respectively. An item is chosen at random.
Find the probability that the item is defective.
Given that the item is defective, find the probability that it was made by machine C.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 311000 (0.4)(0.02) + (0.35)(0.03) + (0.25)(0.05) (M1)(A1) 0.031 = 311000 A1 | 3 |
| (b) | 2562 P(C ∩ D)P(D) (M1) 0.01250.031 (A1) 2562 A1 | 3 |
A bag contains 3 red and 4 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) | 17 37 × 26 (M1) 17 A1 | 2 |
| (b) | 15 P(at least one red) = 1 − P(both blue) (M1) conditional probability formula (M1) 15 A1 | 3 |
The probability that a seed germinates is 0.3. 15 seeds are planted.
Find the probability that exactly 4 germinate.
Find the probability that more than 4 germinate.
Find the expected number of seeds that germinate and the variance.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 0.219 B(15, 0.3) (M1) 0.219 A1 | 2 |
| (b) | 0.485 1 − P(X ≤ 4) (M1) 0.485 A1 | 2 |
| (c) | 4.50; 3.15 E = 4.50 A1 Var = 3.15 A1 | 2 |
A data set of 15 values has mean 15 and standard deviation 3.
One further value, x, is added to the data set and the mean becomes 14. Find x.
Each of the original 15 values is multiplied by 2 and then has 4 added. Write down the new mean and the new standard deviation.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | −1 total of original values = 225 (A1) 225 + x16 = 14 (M1) x = −1 A1 | 3 |
| (b) | mean 34, sd 6 mean 34 A1 standard deviation 6 (unaffected by adding a constant) A1 | 2 |
In the SL & HL syllabus, Statistics & Probability covers Descriptive statistics, Correlation & regression, Probability, Discrete random variables, Binomial distribution, Normal distribution, Bayes' theorem, Continuous random variables.
This page has 10 Statistics & Probability questions with answers. For more, the free generator on mentorriyaz.in builds a new Statistics & Probability paper with a full mark scheme each time you click.
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