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O Level & A Level Mathematics (Cambridge)

A Level Maths — Probability and Statistics 1, Set 2

Take the A Level Maths — Probability and Statistics 1, Set 2: 20 multiple-choice questions (30 minutes) with instant scoring and a full answer review.…

What this test covers

Sample questions with answers

The first 5 questions of this test, with the correct answer and explanation.

  1. Q1. In how many ways can 7 different books be arranged on a shelf?

    • A. 5040 ✓
    • B. 720
    • C. 49
    • D. 2520

    Answer: A. 5040

    Explanation: 7! = 5040.

  2. Q2. In how many ways can 2 people be chosen from 10?

    • A. 90
    • B. 100
    • C. 20
    • D. 45 ✓

    Answer: D. 45

    Explanation: ¹⁰C₂ = 45.

  3. Q3. How many different arrangements are there of the letters of the word COFFEE?

    • A. 90
    • B. 360
    • C. 720
    • D. 180 ✓

    Answer: D. 180

    Explanation: 6!/(2! × 2!) = 180 (two Fs and two Es).

  4. Q4. A committee of 4 is chosen from 5 men and 4 women. In how many ways can it contain exactly 2 women?

    • A. 126
    • B. 60 ✓
    • C. 120
    • D. 36

    Answer: B. 60

    Explanation: ⁴C₂ × ⁵C₂ = 6 × 10 = 60.

  5. Q5. X ~ B(6, 0.5). Find P(X = 3).

    • A. 0.1563
    • B. 0.25
    • C. 0.3125 ✓
    • D. 0.5

    Answer: C. 0.3125

    Explanation: ⁶C₃ × 0.5⁶ = 20/64 = 0.3125.

The other 15 questions

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  1. Q6. X ~ B(5, 0.2). Find P(X = 0), to 3 significant figures.

    • A. 0.8
    • B. 0.2
    • C. 0.328
    • D. 0.410

  2. Q7. X ~ B(n, p) has mean 4 and variance 3. Find n.

    • A. 7
    • B. 12
    • C. 4
    • D. 16

  3. Q8. X ~ Geo(0.4). Find P(X ≤ 2).

    • A. 0.64
    • B. 0.24
    • C. 0.36
    • D. 0.4

  4. Q9. X takes four values with probabilities 0.1, k, 0.3 and 0.2. Find k.

    • A. 0.3
    • B. 0.2
    • C. 0.4
    • D. 0.6

  5. Q10. X takes the values 0, 1 and 2 with probabilities 0.25, 0.5 and 0.25. Find E(X).

    • A. 0.5
    • B. 1.5
    • C. 2
    • D. 1

  6. Q11. X ~ N(100, 15²). What is P(X < 100)?

    • A. 0.15
    • B. 0.8413
    • C. 0.5
    • D. 1

  7. Q12. X ~ N(60, 10²). Find P(X > 75).

    • A. 0.0228
    • B. 0.9332
    • C. 0.1587
    • D. 0.0668

  8. Q13. X ~ N(20, σ²) and P(X < 26) = 0.8413. Find σ.

    • A. 6
    • B. 0.84
    • C. 1
    • D. 26

  9. Q14. X ~ B(100, 0.4). What are the mean and variance of the approximating normal distribution?

    • A. Mean 60, variance 24
    • B. Mean 40, variance 24
    • C. Mean 40, variance 40
    • D. Mean 40, variance 4.9

  10. Q15. Using a normal approximation Y to a binomial X, which probability replaces P(X ≥ 45)?

    • A. P(Y > 45.5)
    • B. P(Y < 44.5)
    • C. P(Y > 44.5)
    • D. P(Y > 45)

  11. Q16. P(A) = 0.5, P(B) = 0.3 and P(A ∩ B) = 0.1. Find P(A ∪ B).

    • A. 0.15
    • B. 0.7
    • C. 0.9
    • D. 0.8

  12. Q17. A and B are mutually exclusive. What is P(A ∩ B)?

    • A. 0
    • B. P(A) + P(B)
    • C. P(A) × P(B)
    • D. 1

  13. Q18. The mean of 8 values is 15. One value, 22, is removed. What is the mean of the remaining 7?

    • A. 15
    • B. 14
    • C. 13
    • D. 16

  14. Q19. For 10 values, Σ(x − 10) = 20 and Σ(x − 10)² = 140. Find the variance of x.

    • A. 4
    • B. 10
    • C. 12
    • D. 14

  15. Q20. In a positively skewed distribution, how does the mean usually compare with the median?

    • A. The mean is greater than the median
    • B. The mean is less than the median
    • C. The mean is always zero
    • D. They are always equal