Lesson 2.03e

2.03e Modelling with probability: Modelling with probability (2.03e) Quiz: OCR Maths, Unit 13

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 2.03e, Modelling with probability: Modelling with probability (2.03e): 20 multiple choice questions for the OCR Maths (H240), Unit 13: Probability, written with Revision Ninja.

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The 20 questions

  1. What key feature must be clearly stated when setting up a mathematical probability model?

    • Hypotheses
    • Assumptions
    • Raw data
    • Confidence intervals

  2. Which assumption underlies P(A and B) = P(A) P(B)?

    • Independence
    • Normality
    • Equal probabilities
    • Mutual exclusivity

  3. What is the assumed probability of rolling a six on a fair six-sided die?

    • 1/3
    • 1/6
    • 1/12
    • 1/2

  4. How can a probability model be made more realistic when conditions change between trials?

    • Increase sample size
    • Vary success probabilities
    • Fix success probabilities
    • Assume independence

  5. What determines the validity and accuracy of predictions made by a probability model?

    • Decimal precision
    • Sample size
    • Underlying assumptions
    • Formula choice

  6. In n independent trials, each with success probability p, what is the expected number of successes?

    • np
    • n/p
    • n + p
    • p^n

  7. Which model fits a fixed number of independent trials, each with the same success probability?

    • Binomial distribution
    • Contingency table
    • Exponential distribution only
    • Uniform distribution only

  8. A batch of 200 items is made with a 5% defect rate, assuming independence. What is the expected number of defects?

    • 40
    • 0.25
    • 10
    • 5

  9. Each customer independently buys with probability 0.3. What is the probability that two customers both buy?

    • 0.3
    • 0.7
    • 0.6
    • 0.09

  10. If storms cause late buses to cluster, what effect does an independence assumption have on consecutive lates?

    • Underestimates consecutive lates
    • Overestimates consecutive lates
    • Maximises variance
    • No effect

  11. If students copy quiz answers, what effect does assuming independence have on predicted matching answers?

    • Underestimates matching answers
    • Zeroes the probability
    • No effect
    • Overestimates matching answers

  12. A player wins each round with probability 0.4, rounds are independent, and 3 rounds are played. What is the probability of exactly 2 wins?

    • 0.12
    • 0.288
    • 0.16
    • 0.432

  13. The chance of rain on any day is 0.3, independently. What is the probability of no rain on three days?

    • 0.027
    • 0.973
    • 0.7
    • 0.343

  14. Each of 5 sensors fails independently with probability 0.02. Approximately what is the probability that at least one fails?

    • 0.096
    • 0.02
    • 0.2
    • 0.904

  15. Why can two mutually exclusive events A and B not have probabilities P(A) = 0.6 and P(B) = 0.7?

    • Sum equals 0
    • Product equals 0
    • Sum exceeds 1
    • Product exceeds 1

  16. A fair coin is tossed repeatedly. What is the probability that the first head occurs on the third toss?

    • 1/8
    • 1/4
    • 3/8
    • 1/3

  17. A player wins each of 4 independent games with probability 0.5. What is the probability of winning all four?

    • 0.5
    • 0.25
    • 0.125
    • 0.0625

  18. If P(A) = 0.5 and P(B) = 0.4, what is P(A and B) under independence?

    • 0.2
    • 0.1
    • 0.3
    • 0.9

  19. A fair die is rolled four times. What is the probability of at least one six?

    • 4/6
    • 625/1296
    • 1/6
    • 671/1296, about 0.518

  20. Two independent components work with probabilities 0.9 and 0.8. What is the probability that at least one works?

    • 1.7
    • 0.72
    • 0.98
    • 0.8

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