Probability Basics and the Probability Scale
Probability is a measure, between 0 and 1, of how likely an event is to happen, and the probability scale is a number line running from 0 (impossible) to 1 (certain) that is used to show and compare likelihoods. Probabilities can be written as fractions, decimals or percentages, and this idea underpins every topic in the Probability strand of GCSE Statistics.
Before you start
No specific prerequisites - this is a good place to start.
Method
- Identify the total number of equally likely outcomes for the experiment.
- Identify how many of those outcomes count as a success for the event you want.
- Write the probability as (number of successful outcomes) divided by (total number of outcomes), and simplify the fraction.
- Convert the fraction to a decimal or percentage if the question asks for one.
- Mark the probability on a 0 to 1 scale, remembering that 0.5 means the event is exactly as likely to happen as not (evens).
- Check the value makes sense: every probability must be between 0 and 1 inclusive.
Worked example
A bag contains 5 red counters, 3 blue counters and 2 green counters. One counter is picked at random. Find the probability that it is blue, giving your answer as a fraction, decimal and percentage.
- Total counters = 5 + 3 + 2 = 10.
- Blue counters = 3.
- P(blue) = 3/10.
- As a decimal, 3/10 = 0.3.
- As a percentage, 0.3 = 30%.
- Final answer: P(blue) = 3/10 = 0.3 = 30%.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1A fair coin is flipped once. What is P(heads)?Show answer
Answer: 1/2 (0.5)
Q2A fair six-sided dice is rolled. What is P(rolling a 5)?Show answer
Answer: 1/6
Q3A bag has 4 yellow and 6 white balls. What is P(picking a yellow ball)?Show answer
Answer: 2/5 (4/10 simplified)
Q4An event has a probability of 0.2 of happening. What is the probability that it does not happen?Show answer
Answer: 0.8 (1 - 0.2)
Q5A spinner has 8 equal sections numbered 1 to 8. What is P(the spinner lands on a number greater than 5)?Show answer
Answer: 3/8 (numbers 6, 7 and 8)
Q6The probability that a train is late is 0.15. Out of 200 trains, how many would you expect to be late?Show answer
Answer: 30 trains (0.15 x 200)
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
A box contains 12 chocolates: 7 dark and 5 milk. One chocolate is chosen at random. Work out the probability that it is milk chocolate, giving your answer as a fraction in its simplest form.
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The probability that it rains on a given day in April is 0.35. (a) Write down the probability that it does not rain. (b) Out of 30 days in April, work out the expected number of rainy days.
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A spinner has sections coloured red, blue, green and yellow. The probabilities of landing on red, blue and green are 0.3, 0.25 and 0.2. (a) Work out the probability of landing on yellow. (b) The spinner is spun 400 times. Work out the expected number of times it lands on yellow.
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See real GCSE Statistics past-paper questions, with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the probability basics and the probability scale worksheet pack - 14 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 16 of GCSE Statistics Foundation Workbook 2 and chapter 22 of GCSE Statistics Higher Workbook 2, the whole course as one free printable PDF.
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