GCSE Maths → Probability → Probability Basics
Probability Basics GCSE Maths
Probability is the maths of chance. It tells us how likely something is to happen. GCSE probability questions often involve fractions, decimals, percentages, sample spaces, tree diagrams, and Venn diagrams.
This page covers the core probability skills students need before moving on to harder probability topics.
Video explanation
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What is probability?
Probability measures how likely an event is to happen. It can be written as a fraction, decimal, or percentage.
The probability scale
- 0 means impossible.
- 1 means certain.
- 1/2 means equally likely.
Example 1: Probability of rolling a 6
A fair dice has 6 possible outcomes: 1, 2, 3, 4, 5, and 6.
Only one outcome is a 6.
Example 2: Probability of an even number
A fair dice has three even numbers: 2, 4, and 6.
Writing probabilities as fractions
At GCSE, probabilities are often written as fractions. The denominator is the total number of possible outcomes.
Example 3: Counters in a bag
A bag contains 3 red counters and 5 blue counters. One counter is chosen at random. Find the probability of choosing a red counter.
Total counters:
Red counters:
Probability:
Converting probability to decimals and percentages
A probability can be written as a fraction, decimal, or percentage.
Example 4: Convert 1/4
Example 5: Convert 3/5
Probabilities that add to 1
If there are only two possible outcomes, their probabilities add to 1.
Example 6: Probability of not raining
The probability of rain is 0.3.
The probability of no rain is:
Example 7: Probability of not choosing red
The probability of choosing red is 2/5.
The probability of not choosing red is:
Expected outcomes
Expected outcomes estimate how many times something should happen over many trials.
Example 8: Expected number of sixes
A fair dice is rolled 60 times. How many sixes would you expect?
You would expect about 10 sixes.
Common mistakes in probability
- Writing probabilities greater than 1.
- Forgetting to simplify fractions.
- Using the number of favourable outcomes as the answer without dividing by the total.
- Confusing probability with percentage.
- Forgetting that probabilities of all outcomes add to 1.
Practice questions
- What is the probability of rolling a 3 on a fair dice?
- What is the probability of rolling an odd number on a fair dice?
- A bag has 4 red counters and 6 blue counters. What is P(red)?
- The probability of passing a test is 0.8. What is the probability of not passing?
- Convert 1/5 to a decimal and percentage.
- A spinner has probability 1/4 of landing on red. It is spun 80 times. How many reds would you expect?
Answers
- 1/6
- 3/6 = 1/2
- 4/10 = 2/5
- 0.2
- 0.2 and 20%
- 20
Probability basics FAQ
What is probability?
Probability is a measure of how likely something is to happen. It is usually written as a fraction, decimal, or percentage.
What is the probability scale?
The probability scale goes from 0 to 1. A probability of 0 means impossible, and a probability of 1 means certain.
Can probability be more than 1?
No. A probability cannot be less than 0 or greater than 1.
Is probability on GCSE maths?
Yes. Probability appears on GCSE maths papers and connects with fractions, decimals, percentages, tree diagrams, Venn diagrams, and sample spaces.
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