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NSW SelectiveYear 7 entry

Probability for the Selective maths test

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Probability is how likely something is, written as favourable outcomes over all possible outcomes. For Selective maths, your child counts every outcome in an organised list, counts the ones wanted, then writes and simplifies the fraction.

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The full lesson is in the SelectiveReady app. A free account opens How and Why Authors Write; this lesson needs a paid plan.

Updated 16 October 2026 · Facts checked 12 October 2026

Probability & Counting (lesson preview)

A short preview from the SelectiveReady lesson “Probability & Counting”, on probability for the NSW Selective test.

Published:

Read the video transcript

Okay, here's our question. We've got a bag of coloured balls. We need to find the probability of picking a blue one. So how would you start? Think back to tool number one. Let's break it right down. First things first, we need the total number of outcomes. That means counting all the balls. So three red plus two blue plus five green, that's 10. That number, 10, is our denominator. Next, we count the favourable outcomes, the ones we're hoping for. We want a blue ball, and there are two of those. So that's our numerator. Now we just write the fraction, two out of 10. But wait, don't forget to simplify. Two out of 10 simplifies down to one over five. And there it is. The probability of picking a blue ball is one in five. See, it's really just counting and then putting those numbers in the right places. Not so bad, right?

Probability & Counting is a full lesson in the SelectiveReady app, with English and Chinese captions on this preview. A free account opens one lesson, How and Why Authors Write; the other lessons need a paid plan1SelectiveReady · 13 October 2026 · Published.

2

What will your child learn in this lesson?

Your child learns the lesson's big secret: if you can count, you can do probability. They'll be able to place a chance on a scale, write it as a fraction, list outcomes without missing any, and count combinations by multiplying.

The clip finds the chance of picking a blue ball from a bag of red, blue and green balls. The full lesson adds the scale, the three tools, three traps and a cheat sheet.

3

What is probability?

Probability measures how likely something is. It runs from 0, which means impossible, to 1, which means certain. Everything else sits in between as a fraction, decimal or percentage.

On the scaleWhat it meansOur example
0ImpossibleRolling a 7 on a normal dice
Less than 1/2UnlikelyTaking a red sock when only 1 sock in 10 is red
1/2Even chanceA coin landing heads
More than 1/2LikelyNot rolling a 6 on a dice
1CertainTaking a blue marble from a bag of only blue marbles

The lesson's comparison is a bag of mixed lollies. You reach in without looking: the chance of red depends on how many red lollies there are compared with all of them.

4

How do probability questions show up in the Selective test?

In our practice sets, they sit inside a picture: a spinner, a bag of marbles, a set of cards or a short list of choices. The Department doesn't list topics, so the number of chance questions in a test isn't published. 2NSW Education · 13 October 2026 · Published

The Department's ruleWhat it means for probability
Questions use concepts your child already learns at school2NSW Education · 12 October 2026 · PublishedChance and fractions are school maths
No calculator2NSW Education · 12 October 2026 · Published in any sectionSimplifying fractions by hand matters
52NSW Education · 12 October 2026 · Published options per questionOptions may show the same chance in different forms, so simplify before matching
The practice papers say there are no marks lost for incorrect answers3NSW Education · 13 October 2026 · PublishedA fraction that's close and makes sense is worth choosing
5

What are the three probability tools?

The lesson's toolkit has three tools: the probability fraction, an organised list and counting combinations. The first one starts every question.

Favourable over total: favourable outcomes on top, all possible outcomes below, and three chance words: impossible, even chance, certain.

  1. Count the total

    Every possible outcome, every colour, every group. This number goes on the bottom.

  2. List in order

    Use a table, a tree diagram or an organised list, so no outcome is missed or counted twice.

  3. Count the favourable outcomes

    The ones the question wants. This number goes on the top.

  4. Write, simplify and check

    Favourable over total, simplified. The answer must be between 0 and 1.

Counting combinations is the shortcut for big lists. With 3 shirts and 2 pairs of pants, there are 3 × 2 = 6 outfits. The lesson's rule: just multiply.

6

What does a worked probability question look like?

We wrote this question to show the tools working together.

Question: A canteen meal deal has one sandwich (ham, cheese or egg) and one drink (juice or milk). Ming's meal is chosen at random. What is the chance it has cheese or milk, or both?

StepWhat your child does
Count the total3 sandwiches × 2 drinks = 6 meals
List in orderHam–juice, ham–milk, cheese–juice, cheese–milk, egg–juice, egg–milk
Count the favourableMeals with cheese or milk: ham–milk, cheese–juice, cheese–milk, egg–milk. That's 4
Write the fraction4/6
Simplify and check4/6 = 2/3, which is between 0 and 1

The list is what makes this safe. Adding the chance of cheese (1/3) to the chance of milk (1/2) gives 5/6, because cheese–milk gets counted twice.

7

Which probability traps catch children out?

The biggest trap is a wrong total. In the clip's bag of 3 red, 2 blue and 5 green, it's easy to add only the first two colours and get 5 instead of 10.

TrapWhat it looks likeThe fix
Missing a groupTotal of the bag counts red and blue onlyAdd every group before writing the bottom number
At least one vs exactly oneCounting meals with both when the question says exactly oneNote the words at least or exactly
Messy listingOutcomes written at random, one missedKeep one choice fixed and change the other
Comparing with the rest3 blue out of 12 others written as 3/12The bottom number is all outcomes, blue included
8

Can my child try one on their own?

Here is a question from our free maths set: a bag of marbles, taken out and put back many times. Your child finds the chance first, then the expected number.

Practice question · SEL-MA-TST-29

The table shows the marbles in Ji-woo's bag.

ColourNumber of marbles
Red6
Blue3
White6

Ji-woo takes a marble without looking, writes down its colour and puts it back. She does this 60 times.

About how many times would you expect her to take a blue marble?

  1. A

    12

  2. B

    15

  3. C

    20

  4. D

    30

  5. E

    48

Show answer and explanation

Answer: A

Answer: A (12)

  1. There are 6 + 3 + 6 = 15 marbles, and 3 of them are blue.
  2. The chance of blue each time is 3/15 = 1/5.
  3. In 60 tries, expect about 1/5 of 60 = 12 blue marbles.

Why the other options are wrong

  • B (15): This compares the 3 blue marbles with the 12 other marbles (3/12 = 1/4) instead of with all 15.
  • C (20): This treats the three colours as equally likely, but there are fewer blue marbles than red or white.
  • D (30): This treats blue and not blue as equally likely, like tossing a coin.
  • E (48): This is how many times you would expect a marble that is not blue.

  1. Count the total

    6 + 3 + 6 = 15 marbles, and 3 of them are blue.

  2. Write the chance

    3/15, which simplifies to 1/5.

  3. Scale it up

    In 60 tries, expect about 1/5 of 60, which is 12. The answer is A.

  4. Check the traps

    B compares blue with the other 12 marbles. C treats the three colours as equally likely.

9

Questions parents ask about probability

What is a favourable outcome?

The result the question asks about. Picking a blue ball is favourable when the question asks for blue.

What does expected mean in a probability question?

About how often something should happen over many tries. The chance times the number of tries gives it.

When should my child use a tree diagram?

When there are two or more steps, like a coin then a spinner. Each branch is one outcome to count.

How can my child practise at home?

Play board games and card games, and ask what the chance of the next roll or card is. Then check it over many tries.

Is the full lesson free?

A free account opens one lesson, How and Why Authors Write; the other lessons need a paid plan1SelectiveReady · 13 October 2026 · Published.

Next questions

Selective Mathematical Reasoning →Lesson: Fractions, Decimals & Percentages →Lesson: Reading Charts and Graphs →Free Selective practice test →The NSW Selective test explained →

Sources and checks

  1. SelectiveReady

    SelectiveReady · Checked 13 October 2026

  2. Selective high school practice tests

    NSW Department of Education · Checked 12 October 2026 · Practice materials: personal or non-commercial use only; CC BY 4.0 does not apply (page notice). Page text: CC BY 4.0.

  3. Selective High School Placement Test, Thinking Skills Question Paper, Practice Test 1 (2026 entry practice tests, PDF)

    NSW Department of Education · Checked 13 October 2026 · Practice materials: personal or non-commercial use only; CC BY 4.0 does not apply (page notice). Quoted briefly with credit. Saved text: the cover-page instructions only; the question pages are not stored (W§3.22).

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