Skip to content

Form 3 Probability Practice

Form 3 · 40 practice questions with instant marking and worked solutions.

Probability is an important part of the Form 3 mathematics curriculum. This topic develops sample spaces, equally likely outcomes, complements and checking. Begin by identifying what every number, symbol, diagram and unit represents. Translate the information into a mathematical relationship before calculating. Each line of working should have a purpose. Finally use estimation, substitution, an inverse operation, or a second representation to check the result. This habit separates a misunderstanding from a copying error and makes correction more useful.

A reliable approach to Probability has four stages. First, mark the given information and the quantity required. Second, choose an appropriate representation, property or formula. Third, carry out the operations in a clear order while retaining signs and units. Fourth, return to the original context and decide whether the result is possible. For a graph or table, read the title, scale and labels before using a value. For algebra, inspect brackets, negative signs and the order of operations before simplifying.

The 40 original questions in this topic use a shared mathematical specification in Chinese and English. Difficulty rises from level 1 to level 5. Early questions establish the language and direct skills of Probability; middle questions add two-step reasoning, conversions and common variations; later questions connect ideas and require a deliberate check. In multiple-choice work, calculate before looking at the choices. In fill-in and short-answer work, retain decisive steps. For true-or-false statements, support the decision with a calculation or counterexample.

Effective revision is more than recording a score. After completing the Probability set, group errors by concept tags and decide whether each problem arose from interpretation, forming an expression, calculation, or presenting the answer. Retry the item on a later day without opening the solution, then test the same method with a different value. If the same tag appears repeatedly, return to the explanation and rebuild the concept. If signs or units are the issue, use a fixed pre-submission checklist.

Probability should also connect with the rest of mathematics. Number and algebra supply calculation tools; measurement and geometry give spatial meaning; data handling asks what a result means. A learner who can explain aloud why every step is valid has moved beyond imitation. Estimate a reasonable range, complete an exact solution, and compare the two. Agreement between context, estimate and exact answer is strong evidence that the solution is sound.

This batch adds 20 questions, bringing the topic to 40. The new questions cover controlled variations of different concepts, with paired bilingual conditions, hints, worked solutions and reproducible checks.

Start practising

  1. 1 Basic
    In Probability, calculate $2/7$. Choose the correct answer.
  2. 2 Basic
    In Probability, calculate $3/8$. Give the numerical value only.

  3. 3 Basic
    In Probability, calculate $4/9$. Show the essential working and give the numerical value.

  4. 4 Basic
    In Probability, the value of $1/10$ is 1/5. Is this statement true?
  5. 5 Basic
    A fair spinner has 18 equal-area sectors, of which 5 are yellow. Find the probability of landing on a non-yellow sector (as a fraction in lowest terms). Choose the correct answer.
  6. 6 Basic
    Roll two independent fair six-sided dice. Find the probability of a sum of $10$ (as a fraction in lowest terms). Give the answer only.

  7. 7 Basic
    A game is tried 100 times with 22 wins. Estimate probability using relative frequency. Find the estimated probability of a win (as a fraction in lowest terms). Show the essential working and give the answer.

  8. 8 Basic
    A bag has 6 red and 6 blue balls. Two are drawn at random without replacement. The probability that they are of different colours is 6/11. Is this true?
  9. 9 Standard
    In Probability, calculate $2/6$. Choose the correct answer.
  10. 10 Standard
    In Probability, calculate $3/7$. Give the numerical value only.

  11. 11 Standard
    In Probability, calculate $4/8$. Show the essential working and give the numerical value.

  12. 12 Standard
    In Probability, the value of $1/9$ is 1/9. Is this statement true?
  13. 13 Standard
    A shooter hits the target with probability $\frac{2}{5}$ each time, independently. He shoots 3 times. Find the probability of at least one hit (as a fraction in lowest terms). Choose the correct answer.
  14. 14 Standard
    A fair spinner has 11 equal-area sectors, of which 4 are yellow. Find the probability of landing on a non-yellow sector (as a fraction in lowest terms). Give the answer only.

  15. 15 Standard
    Roll two independent fair six-sided dice. Find the probability of a sum of $9$ (as a fraction in lowest terms). Show the essential working and give the answer.

  16. 16 Standard
    A game is tried 60 times with 51 wins. Estimate probability using relative frequency. The estimated probability of a win is 3/20. Is this true?
  17. 17 Advanced
    In Probability, calculate $2/10$. Choose the correct answer.
  18. 18 Advanced
    In Probability, calculate $3/6$. Give the numerical value only.

  19. 19 Advanced
    In Probability, calculate $4/7$. Show the essential working and give the numerical value.

  20. 20 Advanced
    In Probability, the value of $1/8$ is 1/4. Is this statement true?
  21. 21 Advanced
    A bag has 7 red and 5 blue balls. Two are drawn at random without replacement. Find the probability that they are of different colours (as a fraction in lowest terms). Choose the correct answer.
  22. 22 Advanced
    A shooter hits the target with probability $\frac{1}{3}$ each time, independently. He shoots 3 times. Find the probability of at least one hit (as a fraction in lowest terms). Give the answer only.

  23. 23 Advanced
    A fair spinner has 9 equal-area sectors, of which 4 are yellow. Find the probability of landing on a non-yellow sector (as a fraction in lowest terms). Show the essential working and give the answer.

  24. 24 Advanced
    Roll two independent fair six-sided dice. The probability of a sum of $7$ is 1/6. Is this true?
  25. 25 Challenging
    In Probability, calculate $2/9$. Choose the correct answer.
  26. 26 Challenging
    In Probability, calculate $3/10$. Give the numerical value only.

  27. 27 Challenging
    In Probability, calculate $4/6$. Show the essential working and give the numerical value.

  28. 28 Challenging
    In Probability, the value of $1/7$ is 1/7. Is this statement true?
  29. 29 Challenging
    A game is tried 100 times with 55 wins. Estimate probability using relative frequency. Find the estimated probability of a win (as a fraction in lowest terms). Choose the correct answer.
  30. 30 Challenging
    A bag has 7 red and 4 blue balls. Two are drawn at random without replacement. Find the probability that both are red (as a fraction in lowest terms). Give the answer only.

  31. 31 Challenging
    A shooter hits the target with probability $\frac{1}{5}$ each time, independently. He shoots 3 times. Find the probability of at least one hit (as a fraction in lowest terms). Show the essential working and give the answer.

  32. 32 Challenging
    A fair spinner has 9 equal-area sectors, of which 7 are yellow. The probability of landing on a non-yellow sector is 7/9. Is this true?
  33. 33 Elite
    In Probability, calculate $2/8$. Choose the correct answer.
  34. 34 Elite
    In Probability, calculate $3/9$. Give the numerical value only.

  35. 35 Elite
    In Probability, calculate $4/10$. Show the essential working and give the numerical value.

  36. 36 Elite
    In Probability, the value of $1/6$ is 1/3. Is this statement true?
  37. 37 Elite
    Roll two independent fair six-sided dice. Find the probability of a sum of $6$ (as a fraction in lowest terms). Choose the correct answer.
  38. 38 Elite
    A game is tried 60 times with 44 wins. Estimate probability using relative frequency. Find the estimated probability of a win (as a fraction in lowest terms). Give the answer only.

  39. 39 Elite
    A bag has 7 red and 3 blue balls. Two are drawn at random without replacement. Find the probability that they are of different colours (as a fraction in lowest terms). Show the essential working and give the answer.

  40. 40 Elite
    A shooter hits the target with probability $\frac{2}{5}$ each time, independently. He shoots 2 times. The probability of at least one hit is 16/25. Is this true?

The report lists what you got wrong and why. Only you can see it.

Common mistakes

Common mistakes in Probability

This topic needs particular care with sample spaces, equally likely outcomes, complements and checking. The first mistake is applying a remembered rule before reading all conditions. The second is compressing working so much that a sign, bracket, decimal point or unit disappears. The third is accepting an impossible answer without checking: for example, a probability above one, a negative physical length, an angle outside the geometric constraints, or a result far from the estimate. Separate the conditions, model, calculation and check, and finish by stating what the answer represents.

More Form 3 topics

Form 3 mixed revision → My mistakes →

Keep missing the same type?

Repeating the same mistake usually means an earlier concept never landed. We find that step in the trial lesson.

Book a Trial WhatsApp us
WhatsApp