Introduction to probability: past paper questions

Where the questions come from

• Question 7May/June 2026, paper 11Structured4 marks

  Two fair 4-sided dice have faces numbered 1 to 4. The dice are thrown, and the numbers are multiplied to give a total.

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• Question 5Oct/Nov 2024, paper 13Structured3 marks

  A bag contains 6 red balls, 4 green balls and 2 blue balls. Zia takes a ball from the bag at random. Write down the letter from the probability scale that shows the probability that Zia takes a green ball

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• Question 23Oct/Nov 2023, paper 11Structured1 mark

  The table shows the number of people in a town who are left-handed and the number who are right-handed. Write down the probability that a person, chosen at random, is left-handed.

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• Question 15May/June 2026, paper 11Structured4 marksHas a diagram

  60 people complete a survey about hobbies.

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• Question 7Oct/Nov 2025, paper 12Structured3 marks

  A bag contains 8 discs numbered 1 to 8. A disc is picked at random from the bag. On the probability scale, draw an arrow ( $\downarrow$ ) to show the probability that the number is an even number, label the arrow A

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• Question 12Oct/Nov 2023, paper 13Structured3 marks

  Rama asks a group of students how they travel to school. The table shows the probability of how a student, chosen at random, travels to school. Complete the table.

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• Question 16May/June 2026, paper 32Structured4 marks

  The probability that a team wins a match is 0.4 . The team plays 20 matches. Work out the expected number of matches they win.

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• Question 10Oct/Nov 2025, paper 12Structured1 mark

  A bag contains red balls and green balls. They are in the ratio red balls: green balls = 2:3. A ball is picked at random.

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• Question 19Oct/Nov 2023, paper 13Structured4 marksHas a diagram

  A bag contains these cards. $$\boxed{{\displaystyle 1}}\boxed{{\displaystyle 7}}\boxed{{\displaystyle 3}}\boxed{{\displaystyle 9}}\boxed{{\displaystyle 4}}\boxed{{\displaystyle 5}}\boxed{{\displaystyle 2}}$$ One of these cards is picked at random. Find the probability that the number on the card is greater than 3.

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• Question 20May/June 2026, paper 33Structured4 marksHas a diagram

  The diagram shows a fair spinner. Azra spins the spinner twice. Complete the tree diagram.

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• Question 7Oct/Nov 2025, paper 31Structured3 marksHas a diagram

  A bag contains 6 red balls, 4 green balls and 2 blue balls. Zia takes a ball from the bag at random. The diagram shows a probability scale.

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• Question 3Oct/Nov 2024, paper 33Structured9 marks

  A wedding invitation is in the shape of a rectangle. Draw the lines of symmetry on this rectangle.

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• Question 9Oct/Nov 2023, paper 31Structured11 marksHas a diagram

  Pure gold costs $42 per gram. The fraction of pure gold in an object is measured in carats.

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• Question 14Oct/Nov 2025, paper 31Structured3 marks

  A bag contains red, yellow, blue and green cards. The table shows the probability of taking a red card and a yellow card. The probability of taking a blue card or a green card is in the ratio blue : green = 5 : 2 .

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• Question 11May/June 2024, paper 11Structured3 marks

  Geetha has a box of toys. She picks a toy at random from the box. The probability that she picks a wooden toy is 0.6.

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• Question 5Oct/Nov 2023, paper 32Structured11 marksHas a diagram

  Heidi records the colour of each of 500 cars crossing a bridge. The pie chart shows some of this information. How many cars are red?

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• Question 5Oct/Nov 2025, paper 33Structured3 marks

  The diagram shows a fair 5-sided spinner. The spinner is spun once. Write down the colour the spinner is least likely to land on.

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• Question 8May/June 2024, paper 13Structured1 mark

  In a city, the probability that it will rain today is 0.15. Find the probability that it will not rain today in this city.

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• Question 15May/June 2023, paper 11Structured2 marks

  Eric has four colours of paint. The table shows the probability that he uses each colour.

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• Question 20May/June 2025, paper 31Structured2 marks

  A tin contains red, yellow, green and brown sweets. The table shows some of the probabilities of picking a sweet of each colour at random. Complete the table.

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• Question 2May/June 2024, paper 31Structured15 marksHas a diagram

  Chen asks some people if they prefer a beach, cruise, lake or mountain holiday. The pie chart shows the results. Find the fraction of people who prefer a mountain holiday.

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• Question 12May/June 2023, paper 12Structured2 marks

  A spinner is spun. The possible outcomes are A, B, C or D. The probability of spinning A, C or D is shown in the table. Complete the table.

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• Question 9May/June 2025, paper 32Structured4 marks

  Flo has a bag of counters. She picks a counter at random from the bag. The probability that she picks a green counter is 0.52 .

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• Question 4May/June 2024, paper 32Structured14 marksHas a diagram

  Anton records the number of pets owned by each of 50 families. The table shows some of his results.

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• Question 21May/June 2023, paper 13Structured4 marks

  A spinner has five sides. Each side is painted red, blue, green, yellow or orange. The table shows some of the probabilities of the spinner landing on each colour.

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• Question 6May/June 2025, paper 33Structured1 markHas a diagram

  In a bag of counters, 6 of the counters are blue. The arrow ($\downarrow$) on the probability scale shows the probability of picking a blue counter at random. Work out the total number of counters in the bag.

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• Question 7May/June 2024, paper 33Structured12 marks

  Li spins a fair 6-sided spinner numbered 1 to 6. On the probability scale, draw an arrow ( $\downarrow$ ) to show the probability that the spinner lands on the number 2.

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• Question 9May/June 2023, paper 31Structured6 marksHas a diagram

  Maria spins a fair 7-sided spinner numbered 1 to 7. Explain why the probability that the spinner lands on a prime number is $\frac{4}{7}$.

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• Question 2May/June 2023, paper 32Structured12 marks

  Mika counts the number of letters in each of the 61 words in a paragraph. Some of his results are shown in the table and bar chart. Complete the table and the bar chart.

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• Question 1May/June 2023, paper 33Structured12 marksHas a diagram

  Claudia asks some students to choose their favourite science from biology, chemistry and physics. The pie chart shows the results. Find the percentage of students who choose chemistry.

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