High Impact Tutoring Built By Math Experts
Personalized standards-aligned one-on-one math tutoring for schools and districts
In order to access this I need to be confident with:
Adding and subtracting fractions Adding and subtracting decimalsProbability scale
Here you will learn about the probability scale, including placing the chance of events happening on a probability scale, calculating the chance of events happening and calculating the chance of events not happening.
Students will first learn about probability scale as part of statistics and probability in 7 th grade.
What is the probability scale?
The probability scale is a number line from 0 to 1 where you can place the probability of events occurring. Events range from impossible to certain.
For example, let’s look at the probabilities of a few possible outcomes when a fair 6- sided dice is rolled.
These events are placed on the probability scale below.
![[FREE] Probability Check for Understanding Quiz (Grade 7 to 12)](https://thirdspacelearning.com/wp-content/uploads/2023/07/Probability-check-for-understanding-quiz-listing-image.png)
[FREE] Probability Check for Understanding Quiz (Grade 7 to 12)
Use this quiz to check your grade 7 to 12 students’ understanding of probability. 15+ questions with answers covering a range of 7th to 12th grade probability topics to identify areas of strength and support!
DOWNLOAD FREE [FREE] Probability Check for Understanding Quiz (Grade 7 to 12)
Use this quiz to check your grade 7 to 12 students’ understanding of probability. 15+ questions with answers covering a range of 7th to 12th grade probability topics to identify areas of strength and support!
DOWNLOAD FREEUnderstanding the probability scale
To understand the probability scale, you must be familiar with the positions of fractions and decimals on a number line between 0 and 1.
Here is the 0 to 1 number line split into decimals and fractions.
An event which is impossible would be positioned at 0.
An event which is certain would be positioned at 1.
An event with an even chance of occurring or not occurring would be positioned at \cfrac{1}{2}.
Events where different fractions, decimals or percentages can be used to describe the probability can be positioned onto the probability scale.
What is the probability scale?
Common Core State Standards
How does this relate to 7 th grade math?
- Grade 7 – Statistics and Probability (7.SP.C.5)
Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around \cfrac{1}{2} indicates an event that is neither unlikely or likely, and a probability near 1 indicates a likely event.
How to place events on a probability scale
In order to place events on a probability scale:
- Identify the probabilities on the scale.
- Indicate the probability of the event on the probability scale.
Probability scale examples
Example 1: probability scale
The chance of rain on Tuesday is 35\%. Place the event on the probability scale below. Then describe the probability of each event.
- Identify the probabilities on the scale.
35\% = 0.35. Create a probability scale with 10 divisions so each tick mark represents 0.1.
2Indicate the probability of the event on the probability scale.
The chance of rain is unlikely, since it is between impossible and even chance. This means that it could rain, but the chances of rain are less.
Example 2: probability scale
The probability of choosing a red marble from a bag is \cfrac{9}{10}. Place the event on the probability scale below. Then describe the probability of each event.
Identify the probabilities on the scale.
\cfrac{9}{10}=0.9. Create a probability scale with 10 divisions so each tick mark represents 0.1.
Indicate the probability of the event on the probability scale.
The probability of choosing a red marble is very likely, since it is close to certain. This means that it will probably happen, but it is not a guarantee.
Example 3: probability scale
The team’s probability of winning the game is 0.6. Place the event on the probability scale below. Then describe the probability of each event.
Identify the probabilities on the scale.
Create a probability scale with 10 divisions so each tick mark represents 0.1.
Indicate the probability of the event on the probability scale.
The probability of the team winning is likely, since it is between even chance and certain.
Example 4: probability scale
A spinner is shown below.
Place the events on the probability scale below. Then describe the probability of each event.
Probability Scale:
Identify the probabilities on the scale.
The scale has six divisions, so each line represents \cfrac{1}{6}.
Indicate the probability of the event on the probability scale.
Event D is impossible.
Events C and A are unlikely.
Event B has an even chance.
Example 5: probability scale
A bag has 10 counters in it. 3 of the counters are red, 4 of the counters are blue, 1 of the counters is green and 2 of the counters are yellow.
Place the events on the probability scale below. Then describe the probability of each event.
Probability scale:
Identify the probabilities on the scale.
The scale has 10 divisions, so each tick mark represents 0.1
Indicate the probability of the event on the probability scale.
Event E is impossible.
Even D is very unlikely.
Events A and B are unlikely.
Event C is likely.
Example 6: calculating probability
A bag has 10 counters in it. 2 of the counters are red, 6 of the counters are blue, 1 of the counters is green and 1 of the counters is yellow.
Place the events on the probability scale below. Then describe the probability of each event.
Probability scale:
Identify the probabilities on the scale.
The scale has 10 divisions, so each tick mark represents 0.1.
Indicate the probability of the event on the probability scale.
Event E is impossible.
Events D and A are very unlikely.
Events B and C are likely.
Teaching tips for probability scale
- While worksheets can be helpful, focus on probability lessons and activities that focus on real-life examples and uses of probability.
- When introducing this topic, stick with theoretical probability. As students progress in their understanding, you can introduce experimental probability and relative frequency.
- For learners who attend math tutoring, encourage the tutors to focus on understanding how to determine the scale of a number line and converting between fractions, decimals and percents, before beginning this topic.
Easy mistakes to make
- Writing probabilities as a ratio
Probabilities must be written as a fraction, decimal or percentage. The chance of rolling a 1 on a fair six-sided dice is \cfrac{1}{6}. This cannot be written as a ratio, for example 1:6.
- Having the probability of an event greater than 1
The chance of all outcomes of an event will always add up to one. Therefore a probability as a decimal cannot be greater than 1 or a fraction cannot be improper. For example 1.4 or \cfrac{6}{5} cannot be probabilities.
Practice probability scale questions
1. The chance of snow on Friday is 15\%.
Which probability scale shows the chance of snow on Friday with the correct description?
15\% = 0.15. The number lines have 10 divisions, so each tick mark represents 0.1.
The chance of snow is unlikely, since it is between impossible and even chance. This means that it could snow, but the chances of snow are less.
2. The probability of choosing a green pencil from a pack is \cfrac{7}{10}.
Which probability scale shows the probability of choosing a green pencil from the pack with the correct description?
The number lines have 10 divisions, so each tick mark represents 0.1.
The probability of picking a green pencil is likely, since it is between even chance and certain.
3. The probability of rolling an even number on a fair dice is \cfrac{3}{6}.
Which probability scale shows the probability of rolling an even number on a fair dice with the correct description?
The number lines have 10 or 6 divisions, but either way the probability should be marked in the middle ( at \cfrac{5}{10} or \cfrac{3}{6}).
The probability of rolling an even number is an even chance, because it is exactly half or 50\%.
4. A spinner is shown below. Place the events on the probability scale below.
The probability scale has six equally likely outcomes so each tick mark represents \cfrac{1}{6}. The arrows show the probability of each event.
5. A bag has 10 counters in it. Place the events on the probability scale below.
The probability scale has ten equally likely outcomes so each tick mark represents 0.1. The arrows show the probability of each event.
6. A bag has 10 counters in it. Place the events on the probability scale below.
There are ten counters so you can either represent each counter as 0.1 or \cfrac{1}{10}.
The arrows show the probability of each event.
Probability scale FAQs
The sample space is all possible outcomes for a probability event.
Yes, this describes an event that you know will happen for sure. Such as “the chance of the sun setting today is 100\% or certain.”
The next lessons are
- Compound probability
- Probability distribution
- Units of measurement
Still stuck?
At Third Space Learning, we specialize in helping teachers and school leaders to provide personalized math support for more of their students through high-quality, online one-on-one math tutoring delivered by subject experts.
Each week, our tutors support thousands of students who are at risk of not meeting their grade-level expectations, and help accelerate their progress and boost their confidence.
Find out how we can help your students achieve success with our math tutoring programs.
[FREE] Common Core Practice Tests (3rd to 8th Grade)
Prepare for math tests in your state with these 3rd Grade to 8th Grade practice assessments for Common Core and state equivalents.
Get your 6 multiple choice practice tests with detailed answers to support test prep, created by US math teachers for US math teachers!