A-Level — mathsStandard1 min read

The Binomial Distribution

Model fixed-trial experiments with the binomial distribution at A-Level. Calculate probabilities and use cumulative tables.

Tutor AI Team2026-02-25T01:58:08.630Z

The binomial distribution models the number of successes in $n$ independent trials, each with probability $p$ of success.

Conditions

$X \sim B(n, p)$

$P(X = r) = \binom{n}{r} p^r (1-p)^{n-r}$

$E(X) = np$ , $\text{Var}(X) = np(1-p)$ .

Problem

$X \sim B(10, 0.3)$ . Find $P(X = 3)$ .

$P(X=3) = \binom{10}{3}(0.3)^3(0.7)^7 = 120 \times 0.027 \times 0.0824 \approx 0.267$ .

Solution

Problem

$P(X \leq 2)$ = sum of $P(X=0) + P(X=1) + P(X=2)$ . Or use cumulative binomial tables.

Solution

Test whether $p$ has changed from a claimed value using the binomial distribution as the test statistic.

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#a-level#maths#statistics#binomial#distribution

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