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VICMath MethodsQuick questions

Unit 3

Quick questions on Bernoulli trials and the binomial distribution: VCE Math Methods Unit 3

7short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is the four conditions for a binomial?
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1. Fixed number of trials $n$. 2. Each trial has only two outcomes, success or failure.
What is worked example?
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A biased coin lands heads with probability $0.6$. It is tossed 5 times. Find the probability of exactly 3 heads.
What is including the constant term twice?
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The formula has $\binom{n}{x}$ once. Writing $\binom{n}{x} p^x (1 - p)^{n - x}$ but then "rounding up" the binomial coefficient is a sign of confusion.
What is forgetting independence?
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Drawing balls without replacement breaks independence; the resulting distribution is hypergeometric, not binomial.
What is wrong formula direction?
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$E(X) = n p$, not $E(X) = p$ or $E(X) = n$. Likewise variance has both $n$ and $p(1 - p)$.
What is boundary errors on cumulative probabilities?
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"At least 3" means $X \geq 3$, which is $1 - P(X \leq 2)$. Subtracting $P(X \leq 3)$ instead loses the $P(X = 3)$ term.
What is squaring the standard deviation incorrectly?
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$\mathrm{Var}(X) = n p (1 - p)$; do not omit the $(1 - p)$ factor.

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