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Year 12 · Statistics & Probability

Binomial distribution

Binomial probability counts exactly k successes in n independent trials: nCk × pᵏ × (1 − p)ⁿ⁻ᵏ.

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How to do it

  1. Find n, k and p.
  2. Count the ways with nCk.
  3. Multiply by the probability of one such outcome.

Worked example

A fair coin is tossed 4 times. What is the probability of exactly 0 heads?
P(X = k) = nCk × (½)ⁿ. 4C0 = 1, and (½)⁴ = 1/16: 1/16.
Answer: 1/16

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The trials must be independent with the same p.

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