Lesson 3B.3.1

3B.3.1 Geometric and negative binomial models Quiz: Pearson Edexcel Further Maths, Unit 12

20 questions

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Lesson 3B.3.1, Geometric and negative binomial models: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 12: Geometric and negative binomial distributions, written with Revision Ninja.

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The 20 questions

  1. What is the probability mass function of a geometric random variable X with parameter p?

    • P(X = x) = p^x (1 - p)^(x - 1)
    • P(X = x) = p(1 - p)^x for x = 0, 1, 2, ...
    • P(X = x) = (1 - p)p^(x - 1)
    • P(X = x) = p(1 - p)^(x - 1) for x = 1, 2, 3, ...

  2. What does a geometric random variable count in this specification?

    • The number of successes in n trials
    • The number of trials up to and including the first success
    • The total time until the fifth success
    • The number of failures before the first success

  3. What does a negative binomial random variable X count?

    • The number of successes in r trials
    • The number of trials needed to obtain r successes
    • The probability of r successes in x trials
    • The number of failures before r successes

  4. What are the possible values of a negative binomial random variable X?

    • All real values of x, from negative infinity up to infinity
    • x = 0, 1, 2, ..., r, which includes zero and every value up to r
    • x = r, r + 1, r + 2, ...
    • x = 1, 2, ..., r, counting only up to the number of successes

  5. What is the special case of the negative binomial distribution when r = 1?

    • The uniform distribution
    • The binomial distribution
    • The geometric distribution
    • The Poisson distribution

  6. A geometric distribution has p = 0.2. What is P(X = 3)?

    • 0.064
    • 0.128
    • 0.512
    • 0.16

  7. A geometric distribution has p = 0.1. What is P(first success on the 4th trial)?

    • 0.0729
    • 0.6561
    • 0.1000
    • 0.0900

  8. For a geometric distribution with p = 0.25, what is P(X > 3)?

    • 0.1406
    • 0.4219
    • 0.0469
    • 0.5625

  9. A negative binomial distribution has r = 2 and p = 0.3. What is P(X = 3)?

    • 0.063
    • 0.147
    • 0.126
    • 0.189

  10. A negative binomial distribution has r = 3 and p = 0.4. What is P(X = 3)?

    • 0.064
    • 0.096
    • 0.192
    • 0.024

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

    • 0.1875
    • 0.3125
    • 0.0625
    • 0.25

  12. X ~ NB(r = 3, p = 0.4). What is P(X = 5) to 4 decimal places?

    • 0.2304
    • 0.1382
    • 0.1152
    • 0.0922

  13. A die is rolled until a six appears. What is the probability that more than three rolls are needed?

    • 1/216
    • 91/216
    • 125/216
    • 5/6

  14. A geometric distribution has p = 0.2. What is P(X >= 4)?

    • 0.4096
    • 0.2048
    • 0.512
    • 0.8

  15. X ~ Geo(0.1). What is P(X <= 5) to 4 decimal places?

    • 0.5000
    • 0.5905
    • 0.0590
    • 0.4095

  16. A negative binomial distribution has r = 2 and p = 0.4. What is P(X = 4)?

    • 0.1728
    • 0.0864
    • 0.1152
    • 0.2304

  17. What is the sum of P(X = x) over all x for a geometric distribution?

    • 0
    • 1
    • p
    • 1/p

  18. A fair coin is tossed. What is P(X = 1) for the geometric count of trials to the first head?

    • 1
    • 0.25
    • 0
    • 0.5

  19. Which two parameters define a negative binomial distribution?

    • n (number of trials) and p (probability of success on each trial)
    • r (number of successes) and p (probability of success)
    • mu (the mean) and sigma (the standard deviation) of the distribution
    • lambda (the mean rate) only, with no other parameter needed

  20. A player tries repeatedly with success probability 0.4 per attempt. What is the probability that the first success occurs on attempt 2 or attempt 3?

    • 0.600
    • 0.384
    • 0.240
    • 0.144

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