The Probability Scale
Recognise that probabilities lie on numerical scales of 0 to 1 or 0% to 100% and use estimation to assign probabilities that events occur in a given context, using common fractions, percentages and decimals.
Read this first
Every probability sits between 0 and 1. You can write it as a fraction, a decimal or a percentage.
0 means impossible. 1 means certain. A half sits in the middle.
Words you need
- Probability
- How likely something is.
- Scale
- A line from 0 to 1, or 0% to 100%.
- Outcome
- One thing that could happen.
Worked example
e.g. A bag has 3 red and 1 blue counter. Find the probability of red.
- Count the total. 3 + 1 = 4 counters.
- Count the reds. There are 3.
- Write it as a fraction. 3 out of 4.
- 3/4 is 0.75 or 75%.
- It sits three quarters of the way to certain.
Check your answer sits between 0 and 1. Anything else is wrong.
Practice
The pictures fade as you go. By the last few you are on your own.
1Where does a probability of 1/2 sit?with a picture
AnswerExactly in the middle.
2A bag has 1 red and 9 blue. Find P(red).with a picture
Answer1/10, or 0,1, or 10%.
3Write 1/4 as a percentage.with a hint
Need a hint?
A quarter of 100.
Answer25%.
4P(rain) is 0.3. Find P(no rain).with a hint
Need a hint?
They add to 1.
Answer0.7.
5Find P(even) on a normal die.on your own
Answer3/6, which is 1/2 or 50%.
6What probability means certain?on your own
Answer1, or 100%.
7Why can a probability never be 1.5?on your own
AnswerNothing can be more than certain.
Think about it
1
Why do all the probabilities of an event add to 1?
One good answerSomething must happen, and 1 means certain.
2
Which form is easiest to compare, fractions or percentages?
One good answerPercentages, because they all use the same scale.
Common mistakes
Writing a probability bigger than 1.
The most likely anything can be is certain.
Mixing up the wanted outcomes and the total.
The total always goes on the bottom.