Probability Scale and Simple Outcomes
Probability measures how likely an event is to happen, expressed as a fraction, decimal or percentage between 0 (impossible) and 1 (certain), often shown on a 0-to-1 probability scale. 11+ papers test placing events on this scale, calculating the probability of simple outcomes such as picking a coloured counter or rolling a dice, and using the fact that all possible outcomes' probabilities add up to 1.
Before you start
Make sure you're comfortable with these topics first:
Method
- Identify the total number of equally likely outcomes and the number of outcomes that match what the question asks for.
- Write the probability as a fraction: number of favourable outcomes / total number of outcomes, then simplify it if possible.
- Remember probabilities can also be written as decimals or percentages, and convert between these forms as the question requires.
- Remember the probability of an event NOT happening is 1 minus the probability of it happening.
- Remember all the probabilities of every possible outcome in a situation must add up to 1 (or 100 percent); use this to find a missing probability.
- Place events on a 0-to-1 scale by judging how likely they are relative to 'impossible' (0), 'even chance' (0.5) and 'certain' (1).
Worked example
A bag contains 4 red counters, 5 blue counters and 3 green counters. A counter is picked at random. Work out the probability that it is blue, giving your answer as a fraction in its simplest form.
- Find the total number of counters: 4 + 5 + 3 = 12.
- Find the number of blue counters: 5.
- Write the probability as a fraction: 5/12.
- Check whether 5/12 can be simplified: 5 is prime and is not a factor of 12, so it is already in its simplest form.
Practice questions
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Q1A fair six-sided dice is rolled once. What is the probability of rolling a 4?Show answer
Answer: 1/6
Q2A fair coin is flipped. What is the probability of it landing on heads?Show answer
Answer: 1/2
Q3A bag has 3 yellow and 7 white balls. What is the probability of picking a yellow ball?Show answer
Answer: 3/10
Q4The probability that it rains tomorrow is 0.3. What is the probability that it does not rain?Show answer
Answer: 0.7
Q5A spinner has 4 equal sections: red, blue, green and yellow. What is the probability of NOT landing on red?Show answer
Answer: 3/4
Q6A bag contains only red and blue counters. The probability of picking red is 2/5. What is the probability of picking blue?Show answer
Answer: 3/5
Q7Put these events in order from least likely to most likely: (a) rolling an even number on a fair dice, (b) picking the ace of spades from a full deck of 52 cards, (c) the sun rising tomorrow.Show answer
Answer: (b), then (a), then (c)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A box contains 6 chocolate biscuits, 9 plain biscuits and some ginger biscuits. There are 30 biscuits in total. (a) How many ginger biscuits are there? (b) A biscuit is picked at random. Work out the probability that it is a ginger biscuit, as a fraction in its simplest form.
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A spinner has 8 equal sections numbered 1 to 8. (a) Work out the probability of spinning a number greater than 5. (b) Work out the probability of spinning a factor of 8. Give both answers as fractions in their simplest form.
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Free printable worksheet
Want more practice on paper? Download the probability scale and simple outcomes worksheet pack - 7 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 27 of 11+ Maths Workbook 3, the whole course as one free printable PDF.
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