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O Level & A Level Mathematics (Cambridge)

A Level Maths — Probability and Statistics 1, Set 1

Take the A Level Maths — Probability and Statistics 1, Set 1: 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. How many different arrangements are there of the letters of the word BANANA?

    • A. 60 ✓
    • B. 20
    • C. 120
    • D. 720

    Answer: A. 60

    Explanation: 6!/(3! × 2!) = 720/12 = 60 (three As and two Ns).

  2. Q2. In how many ways can a committee of 3 be chosen from 8 people?

    • A. 24
    • B. 56 ✓
    • C. 512
    • D. 336

    Answer: B. 56

    Explanation: ⁸C₃ = 56.

  3. Q3. In how many ways can 6 people stand in a line?

    • A. 120
    • B. 720 ✓
    • C. 6
    • D. 36

    Answer: B. 720

    Explanation: 6! = 720.

  4. Q4. X ~ B(10, 0.3). What is E(X)?

    • A. 7
    • B. 2.1
    • C. 0.3
    • D. 3 ✓

    Answer: D. 3

    Explanation: E(X) = np = 10 × 0.3 = 3.

  5. Q5. X ~ B(10, 0.3). What is Var(X)?

    • A. 3
    • B. 2.1 ✓
    • C. 0.21
    • D. 9

    Answer: B. 2.1

    Explanation: Var(X) = np(1 − p) = 10 × 0.3 × 0.7 = 2.1.

The other 15 questions

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  1. Q6. X ~ B(4, 0.5). Find P(X = 2).

    • A. 0.25
    • B. 0.5
    • C. 0.0625
    • D. 0.375

  2. Q7. The probability of success on each trial is 0.2. Find the probability that the first success is on the 3rd trial.

    • A. 0.512
    • B. 0.2
    • C. 0.128
    • D. 0.008

  3. Q8. X ~ Geo(0.25). What is E(X)?

    • A. 4
    • B. 3
    • C. 0.75
    • D. 0.25

  4. Q9. X takes the values 1, 2, 3 with probabilities 0.2, 0.5, 0.3. Find E(X).

    • A. 6
    • B. 2
    • C. 2.1
    • D. 1.9

  5. Q10. For the same X (values 1, 2, 3 with probabilities 0.2, 0.5, 0.3), find Var(X).

    • A. 0.49
    • B. 0.7
    • C. 2.1
    • D. 4.9

  6. Q11. X ~ N(50, 4²). What is the z-value for X = 58?

    • A. 8
    • B. 2
    • C. −2
    • D. 0.5

  7. Q12. Using standard normal tables, what is P(Z < 1), to 4 decimal places?

    • A. 0.9772
    • B. 0.1587
    • C. 0.6827
    • D. 0.8413

  8. Q13. Approximately what is P(Z > 1.96)?

    • A. 0.95
    • B. 0.025
    • C. 0.05
    • D. 0.975

  9. Q14. When is the normal distribution a suitable approximation to B(n, p)?

    • A. When n < 10
    • B. When np < 1
    • C. When np > 5 and n(1 − p) > 5
    • D. Only when p = 0.5 exactly

  10. Q15. Using a normal approximation to a binomial X, which probability replaces P(X ≤ 30)?

    • A. P(Y < 29.5)
    • B. P(Y > 30.5)
    • C. P(Y < 30.5)
    • D. P(Y < 30)

  11. Q16. P(A ∩ B) = 0.12 and P(B) = 0.4. Find P(A | B).

    • A. 0.3
    • B. 0.52
    • C. 0.048
    • D. 0.28

  12. Q17. P(A) = 0.5, P(B) = 0.4 and P(A ∩ B) = 0.2. Are A and B independent?

    • A. No, because P(A ∩ B) ≠ 0
    • B. Yes, because P(A) > P(B)
    • C. Yes, because P(A ∩ B) = P(A) × P(B)
    • D. No, because P(A) + P(B) < 1

  13. Q18. For 10 values, Σ(x − 20) = 30. What is the mean of x?

    • A. 3
    • B. 20
    • C. 50
    • D. 23

  14. Q19. For 10 values, Σx = 50 and Σx² = 290. Find the standard deviation.

    • A. 2
    • B. 5
    • C. 29
    • D. 4

  15. Q20. Which rule is commonly used to identify outliers on a box-and-whisker plot?

    • A. Any value above the mean
    • B. More than 2 × the median
    • C. More than 1 × the range from the median
    • D. More than 1.5 × IQR below Q1 or above Q3