Probability — NSW Year 8 Maths
Chance from a roll, draw or spin, complements and experiments, plus Venn diagrams and two-way tables as extension. Six subtopics and 120 practice questions, each with a fully worked solution, aligned to NESA outcome MA4-PRO-C-01.
Probability in NSW Year 8
Probability measures how likely an event is, with 0 meaning impossible and 1 meaning certain. In Year 8, students revisit the favourable-over-total rule with larger sample spaces, use complements as a shortcut, organise two attributes in Venn diagrams and two-way tables, and compare theoretical probability with the results of real experiments.
The six subtopics below begin with probability and complementary events, then cover Venn diagrams and two-way tables, probability problems that need careful counting, and experimental probability. Probability is one of the 14 topics in NSW Year 8 Maths and sits in the Statistics and Probability strand (NESA outcome MA4‑PRO‑C‑01). Venn diagrams and two-way tables go a step beyond Stage 4 and lead into the multistage experiments of Stage 5.
Subtopics
Probability: common questions
How do you calculate probability in Year 8?
When all the outcomes are equally likely, divide the number of favourable outcomes by the total number of outcomes. A spinner with 10 equal sectors, 4 of them green, gives \(P(\text{green}) = \frac{4}{10} = \frac{2}{5}\).
What are complementary events?
An event and its complement cover every outcome with no overlap, so their probabilities add to 1. If the chance that a bus is late is 0.12, the chance that it is not late is \(1 - 0.12 = 0.88\).
How is a Venn diagram used in probability?
Each circle shows one attribute and the overlap shows both. Count the region you need and divide by the total: if 6 of 30 students play both tennis and cricket, \(P(\text{both}) = \frac{6}{30} = \frac{1}{5}\).
Which NESA outcome covers probability?
Probability sits in Stage 4 of the NSW Mathematics K–10 Syllabus (2022) under outcome MA4‑PRO‑C‑01, taught across Year 7 and Year 8. Venn diagrams and two-way tables are Stage 5 content in the syllabus and are included in Year 8 as extension work.
What is experimental probability?
It is the relative frequency from real trials: the number of times an outcome happened divided by the number of trials. If a paper cup lands on its base 63 times in 300 tosses, the experimental probability is \(\frac{63}{300} = 0.21\).