Probability Scale and Simple Events
The probability scale is a number line running from 0, impossible, to 1, certain, with every probability, whether written as a fraction, decimal or percentage, falling somewhere on it, and 0.5, halfway along, marking an even chance. For a simple event with equally likely outcomes, the probability of a particular outcome is the number of ways it can happen divided by the total number of possible outcomes.
Before you start
Make sure you're comfortable with these topics first:
Method
- Decide whether the outcomes of the event are equally likely before calculating anything (for a fair spinner, dice or coin, they usually are).
- Count the total number of possible outcomes.
- Count the number of outcomes that match what the question is asking for (the favourable outcomes).
- Write the probability as (favourable outcomes) divided by (total outcomes), and simplify the fraction fully.
- To mark a probability on the 0 to 1 scale, place 0 at the far left (impossible), 1 at the far right (certain), and 0.5 in the middle (even chance).
- Use the words impossible, unlikely, even chance, likely and certain only as rough descriptions - always give the exact fraction, decimal or percentage when a calculation is possible.
Worked example
A fair 8-sided spinner is numbered 1 to 8. (a) Find the probability that the spinner lands on a number greater than 5. (b) Describe this probability in words.
- List the total possible outcomes: 1, 2, 3, 4, 5, 6, 7, 8, so there are 8 outcomes in total.
- List the favourable outcomes (numbers greater than 5): 6, 7, 8, so there are 3 favourable outcomes.
- Write the probability as a fraction: P(greater than 5) = 3/8.
- Since 3/8 = 0.375, this sits just below the halfway mark of 0.5 on the probability scale.
- Because 0.375 is less than 0.5 but not close to 0, describe this probability in words as unlikely.
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. Write down the probability that it lands on tails.Show answer
Answer: 1/2 (0.5)
Q2A bag contains 12 discs, all the same size: 3 red, 4 blue and 5 green. One disc is picked at random. Find P(the disc is red).Show answer
Answer: 1/4 (3/12)
Q3The probability that it rains tomorrow is 0.9. Describe this probability using one word from: impossible, unlikely, even chance, likely, certain.Show answer
Answer: Likely
Q4A fair 10-sided dice is numbered 1 to 10. Find P(rolling a multiple of 3).Show answer
Answer: 3/10 (the multiples of 3 from 1 to 10 are 3, 6 and 9)
Q5A letter is chosen at random from the word MATHS. Find P(the letter is a vowel).Show answer
Answer: 1/5 (only A is a vowel out of the 5 letters)
Q6An event has a probability of 0. Describe what this means and give an example of such an event.Show answer
Answer: It means the event is impossible - it cannot happen, for example rolling a 7 on an ordinary fair six-sided dice.
Q7A spinner has 6 equal sections coloured red, red, blue, blue, blue, yellow. Find P(the spinner lands on blue).Show answer
Answer: 1/2 (3/6)
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
A box of 20 raffle tickets contains 5 winning tickets and the rest are losing tickets. One ticket is drawn at random. (a) Find the probability that the ticket is a winning ticket. (b) Find the probability that the ticket is a losing ticket.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
The probability that a spinner lands on green is 0.35. (a) Work out the probability that the spinner does not land on green. (b) The spinner is spun 40 times. Work out the expected number of times it does not land on green.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
Four events are described: (i) picking a red ball from a bag that contains only red balls, (ii) rolling an even number on a fair six-sided dice, (iii) picking the ace of hearts from a shuffled standard 52-card deck, (iv) the sun rising tomorrow. (a) State which of these events are certain (probability 1). (b) State which event has a probability closest to 0.5, and give its probability.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
Free printable worksheet
Want more practice on paper? Download the probability scale and simple events 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 22 of KS3 Maths Workbook 2, the whole course as one free printable PDF.
Other cuts of this worksheet:
Next topics
Not quite what you needed?
Tell us what is missing on probability scale and simple events, or which topic to write up next. Every request is read, and we reply to every one.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.