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Binomial And Hyper-geometric Probability MCQs

Binomial And Hyper-geometric Probability MCQs are statistics questions on two discrete probability distributions: the binomial, for repeated independent trials with replacement, and the hypergeometric, for draws without replacement. They help statistics students and lecturer, PPSC and UGC NET candidates master formulas and properties, and each question shows its answer instantly.

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About Binomial And Hyper-geometric Probability MCQs

This category covers the properties and formulas of both distributions. Binomial questions test the two parameters n and p, the fact that p + q = 1, the mean np and variance npq, skewness when p is less than or greater than one half, and symmetry when p = q = 0.5. Hypergeometric questions focus on trials without replacement, dependent trials and the mean formula. Several items require quick numerical calculation, such as variance for n = 20 and p = 3/5.

Probability distributions are a core part of statistics papers at intermediate, degree and master level, and they appear in lecturer, statistical officer and research posts. Questions mix theory and computation, so you need both the formulas and a clear sense of when each distribution applies. Practice helps you choose the right model instantly. Short calculation items reward memorised formulas over lengthy derivations.

Key facts to remember

  • The binomial distribution has two parameters: n, the number of trials, and p, the probability of success.
  • The mean of a binomial distribution is np and its variance is npq.
  • In a binomial distribution, p + q always equals 1.
  • A binomial distribution is symmetrical when p = q = 0.5.
  • In the binomial distribution the mean is always greater than the variance, since q is less than 1.
  • The hypergeometric distribution applies when sampling is done without replacement.

Exams that include Binomial And Hyper-geometric Probability MCQs

Pakistan

  • PPSC (Statistics Lecturer)
  • FPSC
  • SPSC
  • Lecturer tests
  • Statistical Officer tests

India

  • UGC NET
  • ISS (UPSC)
  • State PSC exams

Bangladesh

  • BCS
  • Government job tests
  • University admission tests

How to prepare for Binomial And Hyper-geometric Probability MCQs

  1. Memorise mean np and variance npq, then practise quick calculations such as 20 × 0.6 × 0.4 to find variance instantly.
  2. Remember the rule of thumb: binomial uses replacement or independent trials, hypergeometric uses no replacement and dependent trials.
  3. Learn how skewness depends on p, positive when p is below 0.5 and negative when p is above 0.5.
  4. Compare binomial and Poisson distributions as well, since questions often ask in which distribution mean equals variance.

Frequently asked questions

What is the difference between binomial and hypergeometric distributions?

The binomial distribution describes the number of successes in n independent trials with a constant probability p, as with sampling with replacement. The hypergeometric distribution describes successes when sampling without replacement from a finite population, so trials are dependent and probability changes.

How many Binomial And Hyper-geometric Probability MCQs are on MCQs360?

MCQs360 has 71 MCQs in this category, and each one shows its answer instantly. They are free to practise without registration and are useful for quick revision of formulas before a statistics test. Keep a formula sheet beside you while you practise.

Which exams ask probability distribution MCQs?

These questions appear in statistics lecturer and statistical officer tests through PPSC, FPSC and SPSC in Pakistan. In India they are tested in UGC NET, the Indian Statistical Service and state PSC exams, and in Bangladesh in BCS and statistics-related job tests.

In which distribution are the mean and variance equal?

The mean and variance are equal in the Poisson distribution, where both equal the parameter lambda. In the binomial distribution, the variance npq is always less than the mean np, because q is less than 1.

Last reviewed October 2026