MH HSC 12 Maths

Binomial Distribution

Each concept is a short lesson, then questions until you get three right.

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4 concepts, a short lesson each

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Bernoulli trials

Trials are Bernoulli when there is a fixed number of them, each has only success or failure, they are independent, and the chance of success stays the same

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Bernoulli trialsTrials are Bernoulli when there is a fixed number of them, each has only success or failure, they are independent, and the chance of success stays the sameStart
The binomial probabilityIf $X \sim B(n, p)$ , then $P(X = r) = {}^nC_r\,p^r q^{n - r}$ with $q = 1 - p$ , for $r = 0, 1, \dots, n$ Start
At least, at most and word problemsAdd the needed terms, or use the complement: $P(X \ge 1) = 1 - q^n$ ; read $n$ , $p$ and the event off the word problem firstStart
Mean and variance of a binomial distribution $E(X) = np$ and $\text{Var}(X) = npq$ ; from a given mean and variance, $q = \dfrac{\text{Var}}{\text{mean}}$ , then $p$ and $n$ Start

Practise Binomial Distribution

Once the concepts click, try the questions your exam asks.

Textbook exercisesEvery exercise, with model answers Past board questionsAsked from this chapter, with solutions

Binomial distribution0 of 4

Practise Binomial Distribution