Probability — NSW Year 9 Core Maths
Probability, relative frequency and two-step experiments. Three subtopics and 60 practice questions, each with a fully worked solution, aligned to NESA outcomes MA5-PRO-C-01 and MA4-PRO-C-01.
Probability in NSW Year 9
Probability measures how likely something is, on a scale from \(0\) for impossible to \(1\) for certain. Year 9 Core students revise single-step probability and relative frequency, and then find probabilities for two-step experiments, such as rolling two dice or drawing two counters from a bag, where \(P(A \text{ and } B) = P(A) \times P(B)\) for independent events.
The three subtopics below cover probability, relative frequency and two-step experiments. Probability is one of the 13 topics in NSW Year 9 Core Maths and belongs to the Statistics and Probability strand. The first two subtopics revise the Stage 4 outcome MA4‑PRO‑C‑01, and two-step experiments are Stage 5 Core content under MA5‑PRO‑C‑01. Venn diagrams and two-way tables are studied in Year 9 Advanced. These ideas lead on to conditional probability in Year 10 and to statistics in senior maths.
Subtopics
Probability: common questions
How do you calculate a probability?
Divide the number of favourable outcomes by the total number of equally likely outcomes. A bag with \(4\) red and \(8\) white marbles gives \(P(\text{white}) = \frac{8}{12} = \frac{2}{3}\).
What is the difference between relative frequency and probability?
Theoretical probability is what should happen in a fair experiment; relative frequency is what did happen, the number of times an outcome occurred divided by the number of trials. If a die shows a \(6\) in \(42\) of \(200\) rolls, the relative frequency is \(0.21\), compared with a theoretical \(\frac{1}{6} \approx 0.17\).
What changes when you draw without replacement?
The second draw has one fewer item, so its probability changes. From \(3\) red and \(5\) blue counters, both red with replacement is \(\frac{3}{8} \times \frac{3}{8} = \frac{9}{64}\), but without replacement it is \(\frac{3}{8} \times \frac{2}{7} = \frac{3}{28}\).
Which NESA outcomes cover probability in Year 9?
Single-step probability and relative frequency revise the Stage 4 outcome MA4‑PRO‑C‑01. Two-step experiments with independent and dependent events are Stage 5 Core content under MA5‑PRO‑C‑01. Venn diagrams and two-way tables are studied in Year 9 Advanced.