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QLDMath MethodsQuick questions
Unit 3: Further calculus and statistics
Quick questions on The binomial distribution (QCE Mathematical Methods Unit 3)
14short 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 when is $X$ binomial?Show answer
A random variable $X$ has a binomial distribution if all four conditions hold.
What is the binomial probability formula?Show answer
For $X \sim \mathrm{Bin}(n, p)$ and $k = 0, 1, 2, \ldots, n$,
What is mean and variance?Show answer
For $X \sim \mathrm{Bin}(n, p)$,
What is cumulative probabilities?Show answer
QCAA commonly asks for $P(X \leq k)$, $P(X \geq k)$ or $P(a \leq X \leq b)$ rather than a single $P(X = k)$.
What is paper 1?Show answer
A student answers 4 multiple-choice questions at random, each with 4 options. Let $X$ be the number correct. Find $P(X = 3)$.
What is paper 2?Show answer
A coin biased so that $P(\text{heads}) = 0.6$ is tossed 50 times. Find the probability of getting between 28 and 35 heads inclusive.
What is using the complement?Show answer
A test has 20 multiple-choice questions, each with 5 options. A student answers at random. What is the probability of getting at least one correct?
What is recognition (not binomial)?Show answer
A bag contains 5 red and 5 blue marbles. Three marbles are drawn without replacement. Let $X$ be the number of red marbles drawn. Is $X$ binomial?
What is misidentifying $n$ and $p$?Show answer
The number of trials $n$ is the count of opportunities for success, not the number of items in any other sense. The probability $p$ is the chance of success on one trial.
What is forgetting the binomial coefficient?Show answer
$P(X = k) = p^k (1 - p)^{n - k}$ alone is the probability of one specific sequence with $k$ successes. The coefficient $\binom{n}{k}$ counts how many sequences have that many successes.
What is wrong direction for $P $?Show answer
It is $1 - P(X \leq k - 1)$, not $1 - P(X \leq k)$. The boundary value $k$ belongs in the "at least" event.
What is using BINS for a without-replacement scenario?Show answer
Without replacement violates independence. Methods only handles binomial probability for with-replacement (or effectively independent) trials.
What is computing $E $ as $p$ instead of $np$?Show answer
Forgetting the $n$ factor is the most common Paper 1 mistake on the mean formula.
What is wrong CAS syntax?Show answer
Different calculators use slightly different function names (binomPdf, binomialPdf, etc.) and argument orders. Practise the exact syntax on your model before the IA2.