IB Maths: Analysis and Approaches chapter 4: Statistics and probability MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

66 exam-style questions on Statistics and probability, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

66 questions · 7 topics · 10 per test

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What chapter 4 covers

Ten Statistics and probability questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. A bag has 5 red and 3 blue counters. Two are taken at random without replacement. Find the probability that they are different colours.

  1. A
    15/32
  2. B
    15/56
  3. C
    1/2
  4. D
    15/28
Show answer

Answer: D. P(RB) + P(BR) = (5/8)(3/7) + (3/8)(5/7) = 30/56 = 15/28. Both orders count, and the second draw is out of 7.

2. X takes the values 1, 2, 3, 4 with probabilities 0.1, 0.3, k, 0.2. Find k.

  1. A
    0.4
  2. B
    0.6
  3. C
    0.25
  4. D
    0.2
Show answer

Answer: A. The probabilities must sum to 1: 0.1 + 0.3 + k + 0.2 = 1, so k = 0.4.

3. The regression line of y on x is y = 2x − 3 and the regression line of x on y is x = 0.4y + 3. Find the mean point (x̄, ȳ).

  1. A
    (9, 15)
  2. B
    (15, 9)
  3. C
    (1.5, 0)
  4. D
    (9, 6.6)
Show answer

Answer: A. Both lines pass through (x̄, ȳ). Substituting: x = 0.4(2x − 3) + 3 = 0.8x + 1.8, so 0.2x = 1.8, x = 9 and y = 2(9) − 3 = 15.

4. A and B are independent, P(A) = 0.6 and P(B) = 0.3. Find P(A ∩ B).

  1. A
    0.9
  2. B
    0.18
  3. C
    0.72
  4. D
    0.12
Show answer

Answer: B. For independent events P(A ∩ B) = P(A)P(B) = 0.6 × 0.3 = 0.18. 0.72 is P(A ∪ B).

5. X ~ B(5, 0.2). Find P(X = 2).

  1. A
    0.2048
  2. B
    0.0205
  3. C
    0.04
  4. D
    0.4
Show answer

Answer: A. P(X = 2) = 5C2(0.2)2(0.8)3 = 10 × 0.04 × 0.512 = 0.2048. Leaving out the 10 gives 0.0205.

6. Masses are distributed N(500, 202) grams. Use your GDC to find the proportion between 480 g and 520 g, to 3 significant figures.

  1. A
    0.954
  2. B
    0.341
  3. C
    0.683
  4. D
    0.5
Show answer

Answer: C. 480 and 520 are one standard deviation either side of the mean; P(480 < X < 520) = 0.683. 0.954 is the proportion within two standard deviations.

7. A test has 10 questions, each with 4 options. A student guesses every answer. Find the probability of exactly 3 correct answers.

  1. A
    0.00209
  2. B
    0.776
  3. C
    0.250
  4. D
    0.300
Show answer

Answer: C. X ~ B(10, 0.25): P(X = 3) = 120 × 0.253 × 0.757 = 0.250. 0.776 is P(X ≤ 3), and 0.00209 leaves out 10C3 = 120.

8. X ~ N(30, σ2) and P(X < 25) = 0.2. Find P(25 < X < 35).

  1. A
    0.3
  2. B
    0.6
  3. C
    0.8
  4. D
    0.4
Show answer

Answer: B. 25 and 35 are symmetric about the mean 30, so P(X > 35) = 0.2 too. Then P(25 < X < 35) = 1 − 0.2 − 0.2 = 0.6.

9. X ~ N(100, 152). Given that the z-value with P(Z < z) = 0.9 is 1.2816, find k such that P(X < k) = 0.9.

  1. A
    119
  2. B
    80.8
  3. C
    101
  4. D
    114
Show answer

Answer: A. k = μ + zσ = 100 + 1.2816 × 15 = 119 (to 3 s.f.). Subtracting gives the 10% point, 80.8.

10. A fair coin is tossed three times. Find the probability of at least one head.

  1. A
    3/8
  2. B
    1/2
  3. C
    7/8
  4. D
    3/4
Show answer

Answer: C. Use the complement: P(no heads) = (½)3 = 1/8, so P(at least one head) = 1 − 1/8 = 7/8.

Start the chapter testAbout the IB Maths: Analysis and Approaches test

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Ways to practise this chapter

Statistics and probability: questions students ask

How many Statistics and probability MCQs are there?

66, each with the answer and a short explanation, across 7 topics: SL4.1 Collecting data and sampling, SL4.2, SL4.3 Presenting and summarising data, SL4.4, SL4.10 Correlation and regression, SL4.5, SL4.6 Probability and combined events, SL4.6, SL4.11 Conditional probability and independence, SL4.7, SL4.8 Discrete random variables and the binomial distribution, SL4.9, SL4.12 The normal distribution. Every chapter test draws ten of them, so you can take it many times.

Is the IB Maths: Analysis and Approaches chapter 4 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

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