Lesson N1

N1 Discrete probability distributions and the binomial distribution Quiz: AQA Maths, Unit 11

20 questions

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Lesson N1, Discrete probability distributions and the binomial distribution: 20 multiple choice questions for the AQA Maths (7357), Unit 11: Statistics, written with Revision Ninja.

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The 20 questions

  1. Which set of conditions must hold for a variable to follow a binomial distribution?

    • A fixed number of independent trials, each with the same probability of success
    • Outcomes that can take any real value in an interval
    • A random number of trials with changing probabilities
    • Trials that depend on each other with a fixed probability

  2. For X ~ B(n, p), which expression gives P(X = x)?

    • p^x (1 - p)^x
    • nCx p^(n - x) (1 - p)^x
    • n p^x (1 - p)^(n - x)
    • nCx p^x (1 - p)^(n - x)

  3. In the binomial distribution B(n, p), what does n represent?

    • The number of successes
    • The probability of success
    • The number of trials
    • The number of possible outcomes for each trial

  4. Which notation means X follows a binomial distribution with 10 trials and probability of success 0.3?

    • X ~ B(0.3, 10)
    • X ~ B(10, 0.3)
    • X ~ B(3, 10)
    • X ~ N(10, 0.3)

  5. Which statement about the probabilities of a discrete distribution is always true?

    • Each lies between -1 and 1 and sums to 0
    • They sum to the number of possible values
    • They sum to 1 over all possible values
    • They must all be equal

  6. X ~ B(5, 0.2). What is P(X = 0), to three decimal places?

    • 0.672
    • 0.328
    • 0.410
    • 0.200

  7. X ~ B(4, 0.5). What is P(X = 2)?

    • 0.500
    • 0.625
    • 0.375
    • 0.250

  8. X ~ B(6, 1/3). What is P(X = 1)?

    • 1/3
    • 32/243
    • 6/729
    • 64/243

  9. X ~ B(10, 0.4). What is P(X <= 1), to three decimal places?

    • 0.605
    • 0.040
    • 0.645
    • 0.355

  10. X ~ B(3, 0.5). What is P(X >= 1)?

    • 0.375
    • 0.125
    • 0.875
    • 0.500

  11. A fair coin is tossed 8 times. What is the probability of exactly 5 heads?

    • 3/16
    • 7/32
    • 5/16
    • 1/32

  12. A player hits 60% of shots independently. In 5 shots, what is the probability of exactly 3 hits?

    • 0.6000
    • 0.0768
    • 0.2304
    • 0.3456

  13. X ~ B(4, 0.15). What is P(X = 3), to four decimal places?

    • 0.0034
    • 0.0510
    • 0.4096
    • 0.0115

  14. X ~ B(20, 0.1). What is P(X = 0), to three decimal places?

    • 0.122
    • 0.018
    • 0.270
    • 0.878

  15. X ~ B(3, 0.2). What is P(X >= 2)?

    • 0.384
    • 0.616
    • 0.104
    • 0.896

  16. A fair coin is tossed 6 times. Which is more likely, exactly 3 heads or exactly 2 heads?

    • Neither can occur in 6 tosses
    • Exactly 3 heads, since 20/64 is greater than 15/64
    • They are equally likely at 15/64 each
    • Exactly 2 heads, since 15/64 is greater than 20/64

  17. A factory finds 5% of items defective. In a sample of 20 items, what is the probability of at most 1 defective item?

    • 0.358
    • 0.264
    • 0.736
    • 0.377

  18. X ~ B(3, p). If P(X = 0) = 0.216, what is p?

    • 0.1
    • 0.4
    • 0.216
    • 0.6

  19. X ~ B(4, 0.25). What is P(X = 4)?

    • 0.3164
    • 0.0039
    • 0.0625
    • 0.2500

  20. A binomial model is used for trials drawn without replacement from a small batch. Why might this be inappropriate?

    • The binomial model needs the number of trials to be unknown
    • The binomial model only applies when n is greater than 100
    • The probability of success changes between draws, so trials are not independent
    • Binomial probabilities cannot be calculated for small batches

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