Count every single outcome, not every colour or total, then write the fraction.
Practice test 1 is free. No card needed.
Probability questions are solved by counting the outcomes you want and putting them over all the equally likely outcomes. Children in Year 7 now sit the exam in Year 8 , expected in June 2027.
Checked by the SelectiveReady team on 12 October 2026 · Updated 27 October 2026 · How we check facts
Independent. Not affiliated with the Victorian Department of Education or ACER.
A probability question asks how likely something is, and the answer is a fraction: the outcomes you want over all the outcomes. It sits in the Mathematics part, which shares a 60-minute sitting with Quantitative Reasoning.
The Victorian Department of Education says the knowledge needed in any section is no more than the Year 8 curriculum. These questions need careful counting and simple fractions, worked by hand.
These three are our own questions, from easier to harder: a bag of marbles, two dice and names in a hat. Each one shows the answer and the working, so read them with your child.
As you read, ask your child to list the outcomes each option counts. A missing or doubled outcome shows up straight away on a list.
A bag holds 4 red, 5 blue and 3 green marbles. Kai takes one marble without looking. What is the probability that it is not blue?
Answer: A
Answer: A
Count marbles, not colours. There are 4 + 5 + 3 = 12 marbles, and 4 + 3 = 7 are not blue, so the probability is 7/12. The tempting 2/3 says two of the three colours are not blue, but there are different numbers of each colour, so the colours are not equally likely. 5/12 is the chance it is blue.
Two ordinary six-sided dice are rolled and the two numbers are added. What is the probability that the total is 8?
Answer: B
Answer: B
There are 6 × 6 = 36 equally likely results. A total of 8 comes from 2 + 6, 3 + 5, 4 + 4, 5 + 3 and 6 + 2: five results, so 5/36. The tempting 1/12 treats 2 + 6 and 6 + 2 as the same result, and 1/11 assumes the eleven totals from 2 to 12 are equally likely, which they are not.
Five students, Liam, Mia, Noah, Priya and Sam, put their names in a hat. Two names are drawn at random to choose the class's two speakers. What is the probability that at least one of Mia and Noah is chosen?
Answer: C
Answer: C
List every possible pair: 4 + 3 + 2 + 1 = 10 pairs. Count the pairs with neither Mia nor Noah: Liam–Priya, Liam–Sam and Priya–Sam, which is 3. The other 7 pairs include at least one of them, so 7/10. The tempting 4/5 adds Mia's 4 pairs to Noah's 4 pairs, but the Mia–Noah pair is then counted twice.
Teach your child to count single outcomes, never types, because every probability answer is a count over a count. These steps are ours, drawn from the working in the answers above.
List or count every single outcome: each marble, each dice result, each pair of names. A colour or a total is not one outcome.
Each marble is as likely as any other. Each colour is not, when there are more of one colour.
Draw a 6 by 6 grid. Each cell is one result, so order matters: 2 then 6 is not the same as 6 then 2.
Count the outcomes where neither thing happens. Take them away from the total to find the rest.
Wanted outcomes over all outcomes, then simplify. Check it answers the event asked about, not its opposite.
Each wrong option below counts the outcomes the wrong way: by type, without order, or twice. The check is the same each time: write the outcomes as a list or grid and count them again.
Use a bag of coloured pegs or mixed lollies. Before each draw, ask your child to say the chance as a fraction. Then draw, put it back, and talk about what happened.
Roll two dice many times and tally the totals. It shows why middle totals such as 7 come up far more often than 2 or 12. For names in a hat, list every pair on paper and tick the ones that fit.
Listing outcomes takes time, so check your child can still do it at exam pace. Practice test 1 in our selective entry practice tests is free and follows the real exam's parts and times, with results by skill afterwards.
For more worked items, see our maths sample questions. For the whole part, see VIC selective entry mathematics.
Practice test 1 marks every answer and shows results by skill: what your child already does well and the three skills to work on next.
Practise for the real test
Practice test 1 is free. Then packs from A$109 for 12 months, or A$9 a week, per exam.