Probability — NSW Year 10 Core Maths
From single events to multistage experiments: complements, tree diagrams and dependent events. Six subtopics and 120 questions with worked solutions, aligned to NESA MA5-PRO-C-01.
Probability in NSW Year 10 Core
Probability in Year 10 Core starts by revising the basics from Stage 4: equally likely outcomes, the scale from 0 to 1 and complementary events. Students then move on to experiments with two or more steps, using tables, tree diagrams and the difference between drawing with and without replacement.
The six subtopics below follow that order. Probability is one of the 11 topics in NSW Year 10 Maths Core and sits within NESA's Statistics and Probability strand (NESA outcome MA5‑PRO‑C‑01, with revision of MA4‑PRO‑C‑01). Two-way tables and Venn diagrams are studied in Year 10 Advanced. Multistage probability leads on to the probability and statistics of Stage 6 Standard and Advanced maths.
Subtopics
Probability: common questions
What probability is in Year 10 Core maths?
Year 10 Core probability covers equally likely outcomes, the probability scale, complementary events and multistage experiments with tables and tree diagrams, both with and without replacement.
How are dependent and independent events different?
Independent events do not affect each other, such as tossing a coin twice. Dependent events do: if you take a marble out and do not put it back, the second draw has different chances from the first.
How do you use a tree diagram?
Draw a branch for each outcome at each stage and write its probability on it. Multiply along a path to get the probability of that combined outcome, then add the paths you need. For two heads from two coin tosses, \(\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}\).
Which NESA outcomes cover Year 10 Core probability?
Multistage experiments, dependent and independent events and simulations come under MA5‑PRO‑C‑01, and the basics revise the Stage 4 outcome MA4‑PRO‑C‑01.
Why is 'at least one' found using the complement?
Because 'at least one' covers many outcomes, but its complement, 'none', is a single outcome. For example, the probability of at least one 6 in three rolls of a die is \(1 - \left(\frac{5}{6}\right)^3 = \frac{91}{216}\).