Binomial distribution
X ~ B(n, p). P(X = r) = nCr pr(1−p)n-r. Used for n trials, each with prob p of success.
Y12 Stats. Conditions: n fixed trials, two outcomes (success/failure), constant p, independent. Mean np, variance np(1−p).
Worked examples
X ~ B(10, 0.3): P(X = 4) = C(10,4) × 0.34 × 0.76 ≈ 0.2001.
P(X ≤ 4) = sum of P(X = 0)...P(X = 4) ≈ 0.8497.
Casio: BinomialPD(4, 10, 0.3) and BinomialCD(4, 10, 0.3).
Frequently asked questions
Cumulative tables?
Y12 hypothesis testing uses these. Modern calculators have functions; tables are still in formula booklet.
When does normal approximate binomial?
Large n with p not too close to 0 or 1; rule of thumb np > 5 and n(1-p) > 5.