Probability — NSW Year 10 Advanced Maths
Venn diagrams, two-way tables, conditional probability and multistage experiments with and without replacement. Ten subtopics and 200 practice questions with worked solutions, aligned to NESA outcomes MA5-PRO-C-01 and MA5-PRO-P-01.
Probability in NSW Year 10 Advanced
Probability measures how likely an event is, from 0 for impossible to 1 for certain. Year 10 Advanced students revise the basics, then use Venn diagrams and two-way tables, the addition rule for events that overlap, and conditional probability \(P(A\mid B)\). They also analyse experiments with two or three stages using arrays and tree diagrams, both with and without replacement.
The ten subtopics below start with basic concepts, Venn diagrams and two-way tables, then cover mutually and non-mutually exclusive events and conditional probability, and finish with arrays, tree diagrams, dependent and independent events, and sampling with and without replacement. Probability is one of the 16 topics in NSW Year 10 Advanced Maths and sits within the Statistics and Probability strand (NESA outcomes MA5‑PRO‑C‑01 and MA5‑PRO‑P‑01, with the basics revising MA4‑PRO‑C‑01 from Stage 4). It leads to probability and discrete distributions in Year 11 Advanced.
Subtopics
Probability: common questions
What is conditional probability?
It is the probability of an event given that another event has happened: \(P(A\mid B)=\frac{P(A\text{ and }B)}{P(B)}\). For example, if \(P(A\text{ and }B)=0.12\) and \(P(B)=0.4\), then \(P(A\mid B)=0.3\).
Are mutually exclusive events the same as independent events?
No. Mutually exclusive events cannot happen together, so their joint probability is 0. Independent events do not affect each other, so the joint probability is the product \(P(A)\times P(B)\). Two events with non-zero probabilities cannot be both.
How do you use a tree diagram?
Write the probability on each branch, multiply along each path to get the probability of that outcome, then add the paths that give the result you want. With 3 black and 2 white marbles drawn with replacement, \(P(\text{same colour})=\frac{3}{5}\times\frac{3}{5}+\frac{2}{5}\times\frac{2}{5}=\frac{13}{25}\).
What changes when you sample without replacement?
The numbers left change after each draw, so the second probability depends on the first. From 4 blue and 2 red balls, \(P(\text{two red})=\frac{2}{6}\times\frac{1}{5}=\frac{1}{15}\).
Which NESA outcomes does Probability cover?
Multistage experiments with and without replacement are MA5‑PRO‑C‑01. Venn diagrams, two-way tables and conditional probability are MA5‑PRO‑P‑01, a Path outcome. The basic concepts subtopic revises MA4‑PRO‑C‑01 from Stage 4 of the NSW Mathematics K–10 Syllabus (2022).