The favourable-over-total shortcut depends on equally likely outcomes. Start by deciding what one outcome means. With two dice, ordered pairs are equally likely; the possible sums are not, because different sums can be made in different numbers of ways.
Curriculum checked 2 October 2026 · original practice for selected skills.
You will need: Fractions and systematic counting.
Attempt each task before opening a hint. If you need help, reveal the first hint, then the setup, then compare your written steps with the solution. Finish with the retests without referring back.
For a finite equally likely sample space, probability equals favourable outcomes divided by total outcomes.
The complement ‘not A’ has probability 1−P(A). It can be easier to count a single unwanted result than many wanted ones.
For two independent fair dice, there are 36 ordered pairs. (1,2) and (2,1) are different outcomes even though both have sum 3.
List prime numbers from 1 to 6.
They are 2, 3 and 5; 1 is not prime.
Six faces are equally likely.
Three prime faces give 3/6.
Answer: 1/2
Before moving on: can you explain why your method works, as well as give the answer?
Write a method as well as an answer. The tasks change the reasoning, not just the numbers.
Count physical balls, not colour names.
There are 10 balls in total.
Four balls are red.
4/10=2/5.
Answer: 2/5
Before moving on: can you explain why your method works, as well as give the answer?
Use 1 minus the probability of 6.
P(6)=1/6.
The six has one of six outcomes.
1−1/6=5/6.
Answer: 5/6
Before moving on: can you explain why your method works, as well as give the answer?
List ordered pairs giving 4.
They are (1,3), (2,2) and (3,1).
There are 6 × 6=36 equally likely pairs.
Three pairs give 3/36=1/12.
Answer: 1/12
Before moving on: can you explain why your method works, as well as give the answer?
A tempting claim: “Every named outcome category is equally likely.”
Categories can contain different numbers of equally likely elementary outcomes.
These changed questions test whether you can reconstruct the method. If you use a hint, record where you got stuck and retry later. Completing this small set does not establish full chapter mastery.
Use the yellow count or a complement.
Nine out of 12 balls are not green.
There are 12 balls.
9/12=3/4.
Answer: 3/4
Could you solve this without the earlier example? If not, revisit the first line where you got stuck.
List all ordered pairs.
(1,4), (2,3), (3,2), (4,1).
Four favourable pairs.
4/36=1/9.
Answer: 1/9
Could you solve this without the earlier example? If not, revisit the first line where you got stuck.
If a retest exposed the same error, rewrite the first incorrect step and explain its correction aloud. If both were independent, return to a mixed exercise or a missed paper question. A parent can ask what changed in the method rather than only asking for the answer.
No. A small experiment can vary. The theoretical answers here follow the stated fair-die and uniform-draw models.
Yes. Use the two print buttons above. The question sheet leaves working space and hides solutions; the worked-solutions option includes the solution steps. Your browser can save either view as a PDF.
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