Probability of combined events: past paper questions

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• Question 18May/June 2026, paper 22Structured6 marksHas a diagram

  Marwa has these 10 numbered tiles.

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• Question 20Oct/Nov 2025, paper 21Structured9 marksHas a diagram

  Bag A contains 5 white balls and 3 black balls. Bag B contains 3 white balls and 1 black ball. Two balls are picked at random from bag B without replacement.

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• Question 5Oct/Nov 2024, paper 41Structured9 marks

  A box contains 3 blue pens and 5 red pens. Mia picks a pen from the box at random. Find the probability that she picks a red pen.

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• Question 4Oct/Nov 2023, paper 41Structured11 marks

  Lucia has two fair spinners. Spinner $A$ is five-sided and is numbered 1, 2, 3, 4, 5. Spinner $B$ is nine-sided and is numbered 3, 3, 3, 4, 4, 4, 4, 5, 5.

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• Question 27May/June 2026, paper 23Structured4 marks

  Juan has a bag containing 2 red counters, 3 green counters and 5 blue counters. Juan picks two counters from the bag at random, without replacement. Find the probability that the two counters are different colours.

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• Question 11Oct/Nov 2025, paper 23Structured2 marks

  Sarah rolls a fair 6-sided dice twice. Find the probability she rolls a number greater than 4 both times.

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• Question 8Oct/Nov 2024, paper 42Structured8 marks

  A bag contains 24 coloured beads. Some are red, some are blue and 10 are yellow. One bead is picked at random from the bag.

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• Question 8Oct/Nov 2023, paper 42Structured9 marksHas a diagram

  The diagram shows two fair dice. Dice A is numbered 1, 2, 2, 2, 3, 6. Dice B is numbered 2, 3, 3, 4, 4, 4.

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• Question 25Oct/Nov 2025, paper 23Structured3 marksHas a diagram

  Mahir picks one number at random from the numbers 5, 10 and 15. He then picks one number at random from the numbers 4, 5 and 6. He adds the two numbers.

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• Question 9Oct/Nov 2024, paper 43Structured9 marksHas a diagram

  A bag contains 5 white balls and 3 black balls. Marwan picks a ball from the bag at random and then replaces it. Find the probability that the ball is white.

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• Question 5Oct/Nov 2023, paper 43Structured14 marksHas a diagram

  Indira records the time taken for workers in her company to travel to work. The table and the histogram each show part of this information.

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• Question 16Oct/Nov 2025, paper 42Structured8 marksHas a diagram

  The histogram shows information about the masses of some coconuts. The masses are classified into four categories $A$, $B$, $C$ and $D$. Show that there are 10 coconuts in category $D$.

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• Question 22May/June 2024, paper 21Structured4 marks

  Bag $A$ and bag $B$ each contain red counters and blue counters only. Stephan picks a counter at random from bag $A$ and Jen picks a counter at random from bag $B$. The probability that Stephan picks a red counter is 0.4 .

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• Question 15May/June 2023, paper 21Structured3 marks

  A bag contains 5 green buttons, 2 blue buttons and 6 white buttons. Maya takes two buttons at random from the bag, without replacement. Calculate the probability that one button is green and the other button is not green.

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• Question 17May/June 2025, paper 21Structured7 marks

  A bag contains 6 red marbles, 3 green marbles and 1 blue marble. Two marbles are picked at random from the bag with replacement. Find the probability that both marbles are green.

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• Question 4May/June 2024, paper 41Structured18 marks

  Jianyu records the time, in seconds, that some cars take to travel $195\mathrm{m}$. The box and whisker plot shows this information.

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• Question 23May/June 2023, paper 22Structured3 marks

  Bag $A$ and bag $B$ each contain red sweets and yellow sweets. Anna picks a sweet at random from bag $A$. Ben picks a sweet at random from bag $B$.

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• Question 11May/June 2025, paper 23Structured4 marks

  Angela picks a number at random from the numbers 1, 2 and 3. She then picks a number at random from the numbers 4, 5 and 6. She adds the two numbers to find the total.

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• Question 9May/June 2024, paper 43Structured12 marks

  The diagram shows 7 cards. Amir picks a card at random. Find the probability that the card shows the letter H

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• Question 4May/June 2023, paper 42Structured18 marks

  The table shows information about the heights of 80 children.

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• Question 15May/June 2025, paper 41Structured9 marksHas a diagram

  The height of each of 140 basketball players is recorded. The table shows the results.

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• Question 2May/June 2023, paper 43Structured8 marks

  Anna records the number of text messages she receives for 14 days. 17 15 31 38 31 22 13 18 21 27 28 21 31 29 Complete the stem-and-leaf diagram.

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• Question 16May/June 2025, paper 42Structured4 marks

  On any day, the probability that the weather will be sunny is 0.7. Find the probability that on any day the weather will not be sunny.

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• Question 20May/June 2025, paper 43Structured5 marksHas a diagram

  Stephan has two bags, $A$ and $B$, each containing red sweets and yellow sweets only. He picks two sweets at random, one from bag $A$ and the other from bag $B$. The probability that Stephan picks a red sweet from bag $A$ is $\frac{3}{5}$.

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