Probability
Grade 1-3The Probability Scale
Every probability sits somewhere on a scale from 0, impossible, to 1, certain, and being able to translate between numbers, words and positions on that scale is what these questions test. This lesson covers describing probability in words, reading and marking values on the 0 to 1 scale, and ordering probabilities from least to most likely.
What you need to know
- 0 means impossible, 1 means certain, and 0.5 means an even chance.
- Write probabilities as fractions, decimals or percentages, never as ratios or as 1 in 5.
- Words like unlikely and likely map to positions on the 0 to 1 scale.
- An event and its opposite sit the same distance from each end of the scale.
Written by Asad, co-founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Describing probability in words
Probability can be described using words instead of numbers: impossible (0), unlikely, an even chance (0.5), likely, and certain (1). Only a probability of exactly 0 is impossible, and only a probability of exactly 1 is certain.
A probability of 0.1 is close to 0, so it is best described as unlikely, not impossible, since impossible only applies to a probability of exactly 0.
Reading and marking values on the probability scale
The probability scale runs from 0 at one end to 1 at the other, with 0.5 exactly in the middle representing an even chance. A probability can be read off the scale by finding where it is marked, or a value can be plotted onto the scale at the matching position.
A point marked a fifth of the way along a scale from 0 to 1, between the 0.1 and 0.3 marks, represents a probability of 0.2.
Ordering probabilities
To order a list of probabilities from least to most likely, convert them all to the same form, usually decimals, so they can be compared directly, then arrange them from smallest to largest.
0.3, 0.65, 0.1 and 0.8 in order from least likely to most likely: 0.1, 0.3, 0.65, 0.8.
Matching a calculated probability to a point on the scale
Some questions describe a situation, such as rolling a dice, and ask which labelled point on a scale represents the probability of an outcome. Calculate the probability first, then find the point positioned at that value.
Rolling a fair 6-sided dice, the probability of an even number is 3/6 = 0.5, so the point positioned exactly at 0.5 on the scale represents this probability.
Worked examples
Three exam-style questions, fully solved
The probability that an event happens is 0.1. State whether this is best described as impossible, unlikely, an even chance, likely, or certain.
Easy- 1.Compare 0.1 to the key values on the scale: 0 (impossible), 0.5 (even chance), 1 (certain)
- 2.Recognise that 0.1 is close to 0 but not equal to it
Answer: Unlikely
Put these probabilities in order, starting with the least likely: 0.3, 0.65, 0.1, 0.8
Medium- 1.Compare all four values, which are already in decimal form
- 2.Arrange them from smallest to largest
Answer: 0.1, 0.3, 0.65, 0.8
The probability scale below shows four points, A, B, C and D. A fair 6-sided dice is rolled. Which point best represents the probability that it shows an even number?
Hard- 1.Work out the probability of rolling an even number: 3 out of 6 outcomes are even
- 2.Simplify: 3/6 = 0.5
- 3.Find the point positioned at 0.5 on the scale
Answer: Point C
Practice
6 questions, marked instantly
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Practice
Now try these yourself.
Type your answer and check it. The worked solution appears once you have had a go.
On the probability scale from 0 to 1, what number represents an event that is certain to happen?
On the probability scale, what number represents an impossible event?
Write the probability 1/4 as a decimal.
Write the probability 0.8 as a fraction in its simplest form.
Which is more likely: a probability of 0.35 or a probability of 3/10? Answer 0.35 or 3/10.
The probability a spinner lands on red is 0.45 and on blue is 0.2. What is the probability it lands on neither red nor blue?
Avoid these
The mistakes students make most often
Describing a small but non-zero probability, such as 0.1, as "impossible" instead of "unlikely", since impossible only applies to a probability of exactly 0.
Misreading the position of a value on the scale, especially between the smaller gridlines.
Ordering probabilities by how they look rather than converting them all to a common form, such as decimals, before comparing.
Forgetting to calculate the probability first when a question describes a situation and asks which point on the scale represents it.
Mixing up which end of the scale is 0 and which is 1, leading to values being read or plotted the wrong way round.
FAQ
Questions students and parents ask
Before this topic, make sure you know
What to learn next
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