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The binomial distribution

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Useful for: IB Math AA SL & HL IB Math AI SL & HL AP® Statistics

Learn it With n independent trials, each a success with probability p: P(X = k) = C(n, k)pᵏ(1 − p)ⁿ⁻ᵏ. Mean np, standard deviation √(np(1 − p)).

Example: A basketball player makes 70% of free throws. P(exactly 8 of 10)?

  1. C(10, 8)(0.7)⁸(0.3)² = 45 × 0.0576 × 0.09.
  2. ≈ 0.233.

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