Probability — NSW Year 9 Advanced Maths
Theoretical and experimental probability, Venn diagrams, two-way tables and two-step experiments. Five subtopics and 100 practice questions with fully worked solutions, aligned to NESA outcomes MA5-PRO-C-01 and MA5-PRO-P-01.
Probability in NSW Year 9 Advanced
Probability measures how likely an event is, on a scale from 0 to 1. In Year 9 Advanced, students revise theoretical probability and relative frequency, organise information in Venn diagrams and two-way tables, find conditional probabilities when the group is restricted, and find probabilities for two-step experiments with and without replacement.
The five subtopics below cover probability, relative frequency, Venn diagrams, two-way tables and two-step experiments. Probability is one of the 14 topics in NSW Year 9 Advanced Maths and belongs to NESA's Statistics and Probability strand. It revises the Stage 4 outcome MA4‑PRO‑C‑01 and covers the Stage 5 outcomes MA5‑PRO‑C‑01 and MA5‑PRO‑P‑01. These ideas lead on to experiments with more stages and to probability in Years 11 and 12.
Subtopics
Probability: common questions
What is the difference between probability and relative frequency?
Theoretical probability comes from equally likely outcomes, such as \(\frac{1}{6}\) for rolling a 6. Relative frequency comes from an experiment: 42 sixes in 200 rolls gives 0.21. With more trials, the relative frequency usually gets closer to the probability.
How do you use a Venn diagram to find a probability?
Fill in the overlap first, then the rest of each set, then the region outside both. If 18 of 40 people have a cat, 15 have a dog and 6 have both, then \(18 + 15 - 6 = 27\) have a cat or a dog, so the probability is \(\frac{27}{40}\).
What is conditional probability?
It is a probability worked out within a smaller group. If 12 students play basketball and 5 of them also play soccer, the probability that a basketball player also plays soccer is \(\frac{5}{12}\).
What does without replacement mean?
The first item is not put back, so there is one fewer item for the second draw. With 3 red and 5 blue counters, the probability of two reds without replacement is \(\frac{3}{8} \times \frac{2}{7} = \frac{3}{28}\).
Which NESA outcomes cover probability in Year 9 Advanced?
Simple probability and relative frequency revise the Stage 4 outcome MA4‑PRO‑C‑01. Two-step experiments are the Stage 5 Core outcome MA5‑PRO‑C‑01, and Venn diagrams, two-way tables and conditional probability are the Path outcome MA5‑PRO‑P‑01.