Describe chances as fractions, decimals or percentages and check that possible outcomes account for the whole event.
Foundation and Higher · Useful for students building fluency and applying the method in GCSE questions.
Core pathway. Core GCSE methods are useful across Foundation and Higher. Start with the core examples and questions.
Higher extension. More demanding selections are marked Higher extension: practice questions 6, 8. Use these after the core work, following your teacher’s guidance.
3 worked examples and 8 original practice questions · Allow 25–40 minutes · Read online or print. Higher extensions are labelled. No account or email needed.
Printing includes the method, examples and space for working, followed by a separate answer section.
Adding probabilities works for mutually exclusive alternatives. Multiplying is used for a sequence, with any dependence reflected in the branch values.
Read each line of working and explain why it follows from the previous line.
Divide favourable outcomes by the total number of equally likely outcomes. For the opposite event, subtract its probability from 1.
Probability · Core GCSE skill · No calculator · 1 marks
A fair six-sided dice is rolled once.
Write down the probability that the dice lands on a number less than 3.
Now practise this method: Question 1 · Question 2
Mutually exclusive and exhaustive outcomes have probabilities totalling 1. Use frequencies to estimate a probability when the question gives experimental results. Relative frequency is the observed count divided by the number of trials. An estimated future count is probability multiplied by the number of trials. When the remaining outcomes are in a ratio, share the remaining probability using those ratio parts.
Probability · Core GCSE skill · No calculator · 2 marks
A spinner can land on red, blue, green or yellow.
The table shows the probabilities for three of the colours.
| Colour | red | blue | green | yellow |
|---|---|---|---|---|
| Probability | 0.2 | 0.35 | 0.1 |
Work out the probability that the spinner lands on yellow.
Now practise this method: Question 3 · Question 4 · Question 5
Multiply along each route in a probability tree and add alternative routes. For independent events the second probability does not change; without replacement it may change.
Probability Trees · Core GCSE skill · Calculator allowed · 3 marks
A bag contains 3 red counters and 7 blue counters.
Kira takes a counter at random, notes its colour and puts it back.
She then takes a second counter at random.
Given diagram. A bag contains 3 red counters and 7 blue counters. Kira takes a counter at random, notes its colour and puts it back. She then takes a second counter at random. Complete the probability tree diagram for the two picks. Work out the probability that both counters are blue. Use the labelled information; do not estimate measurements from the sketch.
Worked diagram. A bag contains 3 red counters and 7 blue counters. Kira takes a counter at random, notes its colour and puts it back. She then takes a second counter at random. Complete the probability tree diagram for the two picks. Work out the probability that both counters are blue. Model working: P(red) = ( 3 ) divided by ( 10 ) = 0.3 and P(blue) = ( 7 ) divided by ( 10 ) = 0.7. The counter is replaced, so the second pick has the same probabilities. P(both blue) = 0.7 × 0.7 = 0.49
Now practise this method: Question 6 · Question 7 · Question 8
Write your working on paper. Marks indicate how much working to show; these questions are self-marked and do not change saved practice results. Use squared paper for drawing questions.
Probability · Core GCSE skill · Calculator allowed · 2 marks
Priya buys 12 tickets in a school raffle.
A total of 400 tickets are sold.
One ticket is picked at random to win the prize.
Work out the probability that Priya does not win the prize.
Probability · Core GCSE skill · No calculator · 2 marks
A bag contains 4 green counters, 7 yellow counters and 9 white counters.
A counter is taken from the bag at random.
Find the probability that the counter is not green.
Probability · Core GCSE skill · Calculator allowed · 2 marks
Amy and Ben each spin the same spinner and record how many times it lands on red.
| Number of spins | Number of reds | |
|---|---|---|
| Amy | 50 | 18 |
| Ben | 150 | 42 |
Using all of the results, work out the best estimate for the probability that the spinner lands on red.
Probability · Core GCSE skill · Calculator allowed · 2 marks
The probability that a bus is late on any day is 0.15.
Nadia catches this bus on 40 days.
Work out an estimate for the number of days the bus is late.
Probability · Core GCSE skill · No calculator · 3 marks
A bag contains only red, blue and green counters.
of the counters are green.
The rest of the counters are red and blue in the ratio red : blue = 3 : 2.
A counter is taken from the bag at random.
Work out the probability that the counter is blue.
Probability Trees · Higher extension · No calculator · 3 marks
Femi plays two games of table tennis.
The probability that he wins each game is .
The results of the games are independent.
Work out the probability that Femi loses at least one of the games.
Probability Trees · Core GCSE skill · Calculator allowed · 4 marks
The probability that Jon's bus is on time on any day is 0.9.
Whether the bus is on time on one day is independent of any other day.
Jon catches the bus on Monday and on Tuesday.
Given diagram. The probability that Jon's bus is on time on any day is 0.9. Whether the bus is on time on one day is independent of any other day. Jon catches the bus on Monday and on Tuesday. Complete the probability tree diagram. Work out the probability that the bus is on time on both days. Use the labelled information; do not estimate measurements from the sketch.
Probability Trees · Higher extension · Calculator allowed · 4 marks
Cara and Dan each take a driving test.
The probability that Cara passes is 0.6.
The probability that Dan passes is 0.75.
The two events are independent.
Work out the probability that exactly one of them passes.
Compare the reasoning as well as the final answer. Another correct method is valid. If a step is unclear, revisit an example before trying a similar question.
Worked diagram. The probability that Jon's bus is on time on any day is 0.9. Whether the bus is on time on one day is independent of any other day. Jon catches the bus on Monday and on Tuesday. Complete the probability tree diagram. Work out the probability that the bus is on time on both days. Model working: Each pair of branches sums to 1, so P(late) = 1 - 0.9 = 0.1. P(on time both days) = 0.9 × 0.9 = 0.81
Workouts provide interactive practice; choose the tier your school has recommended.
Give students time to write the method, then compare their working with the answer section. Ask which step they would check first if their answer differs.
Build a custom classroom worksheet or print this page. The teacher builder can display questions on a projector and reveal answers separately.