AS Level Mathematics chapter 3: Probability & Statistics 1 MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

40 exam-style questions on Probability & Statistics 1, 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.

40 questions · 5 topics · 10 per test

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What chapter 3 covers

Ten Probability & Statistics 1 questions with answers

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

1. How many even 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 if no digit is repeated?

  1. A
    840
  2. B
    120
  3. C
    360
  4. D
    720
Show answer

Answer: C. Fix the last digit first: 3 choices (2, 4 or 6). The remaining three places can be filled in 6 × 5 × 4 = 120 ways. Total 3 × 120 = 360.

2. Group A has 10 values with mean 20. Group B has 15 values with mean 30. Find the mean of all 25 values.

  1. A
    25
  2. B
    27
  3. C
    24
  4. D
    26
Show answer

Answer: D. Total of A = 200, total of B = 450. Combined mean = 650/25 = 26. Averaging the two means (25) ignores the different group sizes.

3. Find the number of arrangements of the letters of the word ORANGES that begin and end with a vowel.

  1. A
    360
  2. B
    720
  3. C
    1440
  4. D
    5040
Show answer

Answer: B. There are 3 vowels (O, A, E). The first and last letters can be chosen in 3 × 2 = 6 ways and the other 5 letters arranged in 5! = 120 ways: 6 × 120 = 720. Using C(3, 2) = 3 for the ends ignores their order and gives 360.

4. For a set of 10 values, Σx = 120 and Σx2 = 1690. Find the standard deviation.

  1. A
    25
  2. B
    5
  3. C
    13
  4. D
    2.24
Show answer

Answer: B. Mean = 12. Variance = Σx2/n − mean2 = 169 − 144 = 25, so the standard deviation is √25 = 5. Do not forget to take the square root.

5. X has the distribution N(30, 25). Find P(X < 22), to 3 significant figures.

  1. A
    0.945
  2. B
    0.375
  3. C
    0.0668
  4. D
    0.0548
Show answer

Answer: D. The variance is 25, so σ = 5. z = (22 − 30)/5 = −1.6, and P(Z < −1.6) = 1 − Φ(1.6) = 1 − 0.9452 = 0.0548. Using σ = 25 wrongly gives 0.375.

6. X has the distribution N(μ, 9) and P(X > 50) = 0.1. Find μ, to 3 significant figures.

  1. A
    53.8
  2. B
    46.2
  3. C
    38.5
  4. D
    48.5
Show answer

Answer: B. P(Z > z) = 0.1 gives z = 1.282. Then (50 − μ)/3 = 1.282, so μ = 50 − 3.85 = 46.2. σ is 3 (not 9), and μ must be below 50 since only 10% lies above 50.

7. X has the binomial distribution B(10, 0.3). Find P(X = 2), to 3 significant figures.

  1. A
    0.233
  2. B
    0.0518
  3. C
    0.267
  4. D
    0.383
Show answer

Answer: A. P(X = 2) = C(10, 2) × 0.32 × 0.78 = 45 × 0.09 × 0.05765 = 0.233. Leaving out C(10, 2) gives 0.0518.

8. The probability that it rains on a given day is 0.3. If it rains, the probability that a bus is late is 0.6; if it does not rain, this probability is 0.2. Given that the bus is late, find the probability that it rained.

  1. A
    0.18
  2. B
    0.6
  3. C
    0.32
  4. D
    0.5625
Show answer

Answer: D. P(rain and late) = 0.3 × 0.6 = 0.18; P(late) = 0.18 + 0.7 × 0.2 = 0.32. P(rain | late) = 0.18/0.32 = 0.5625. Divide by the probability of the given event, not by 1.

9. A random variable X has P(X = x) = kx for x = 1, 2, 3, 4. Find the value of k.

  1. A
    1/4
  2. B
    1/24
  3. C
    1/30
  4. D
    1/10
Show answer

Answer: D. The probabilities must add to 1: k(1 + 2 + 3 + 4) = 10k = 1, so k = 1/10.

10. A random variable X takes the values 1, 2, 3 with probabilities 0.2, 0.5, 0.3 respectively. Find E(X).

  1. A
    2
  2. B
    2.1
  3. C
    6
  4. D
    2.5
Show answer

Answer: B. E(X) = Σx P(X = x) = 1 × 0.2 + 2 × 0.5 + 3 × 0.3 = 0.2 + 1.0 + 0.9 = 2.1.

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Ways to practise this chapter

Probability & Statistics 1: questions students ask

How many Probability & Statistics 1 MCQs are there?

40, each with the answer and a short explanation, across 5 topics: Representation of data, Permutations and combinations, Probability, Discrete random variables, The normal distribution. Every chapter test draws ten of them, so you can take it many times.

Is the AS Level Mathematics chapter 3 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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