Probability 1 (AQA GCSE Maths): Revision Notes
Probability 1
What is probability?
Probability measures how likely an event is to happen. The probability that an event will occur is always a value between 0 and 1.
Probability tells you the chance that something will happen. Understanding how to work with probability is essential for making predictions and analysing uncertain situations.
You can express probability in three different ways:
- Fraction (e.g., 1/2)
- Decimal (e.g., 0.5)
- Percentage (e.g., 50%)
All three ways represent the same probability value - they're just different formats for expressing the same concept.
The probability scale
The probability scale runs from 0 to 1, providing a complete range for measuring likelihood. This scale is fundamental to understanding how probability works in practice.
Understanding the probability scale:
- Impossible events have a probability of 0
- Certain events have a probability of 1
- Even chance events have a probability of 0.5 (or or 50%)
Events with probabilities closer to 1 are more likely to happen. Events with probabilities closer to 0 are less likely to happen. This gives you a clear way to compare different events and understand their relative likelihood.
Writing probabilities
When writing probabilities, we use the notation P(event) to mean "the probability of an event happening". This standard mathematical notation helps communicate probability concepts clearly and precisely.
Worked Example: Probability Notation
- The probability of rolling a 6 on a dice is , so we write P(6) =
- The probability of a coin landing heads is , so we write P(Heads) =
This is because there is one head on a coin, and two possible outcomes (heads or tails).
The golden rule
The most important concept in probability is understanding how to calculate the likelihood of any event. This fundamental principle forms the basis of all probability calculations.
The Golden Rule of Probability:
This formula helps you calculate the probability of any event happening. Master this formula and you can solve any basic probability problem.
Worked Example: Dice Rolling
When rolling a standard dice, there are 6 possible outcomes (1, 2, 3, 4, 5, 6).
To find P(rolling a 6):
- Number of successful outcomes = 1 (only one way to roll a 6)
- Total number of possible outcomes = 6
- Therefore: P(rolling a 6) =
Worked Example: Spinner Probability
Looking at this spinner with 8 equal sections, you can calculate probabilities by counting the sections.
If half the sections contain the letter X:
- Number of successful outcomes = 4 (sections with X)
- Total number of possible outcomes = 8 (total sections)
- Therefore: P(landing on X) = = 0.5
This means there is an even chance of landing on X.
Probability vocabulary
Understanding the language of probability is essential for exam success. These terms help you describe and interpret probability values accurately.
Key Probability Vocabulary:
- Impossible - probability = 0 (will never happen)
- Unlikely - probability is close to 0 (probably won't happen)
- Evens - probability = 0.5 (even chance, might happen)
- Likely - probability is close to 1 (probably will happen)
- Certain - probability = 1 (will definitely happen)
Exam tips
Success in probability questions comes from following systematic approaches and avoiding common mistakes.
Critical Exam Reminders:
- Always check that probabilities are between 0 and 1
- Probabilities cannot be negative or greater than 1
- Remember that probabilities are numbers from 0 to 1, not just words
- Count carefully when finding successful and total outcomes
- Show your working using the golden rule formula
Practice approach
When solving probability questions, following a structured method will help you avoid mistakes and ensure you get full marks.
Step-by-Step Problem Solving:
- Identify what event you're finding the probability for
- Count the number of successful outcomes
- Count the total number of possible outcomes
- Apply the golden rule formula:
- Simplify your fraction if possible
Key Points to Remember:
- Probability is always a value between 0 and 1
- Use the golden rule:
- Impossible events have probability 0, certain events have probability 1
- You can write probabilities as fractions, decimals, or percentages
- Learn the probability vocabulary words for describing likelihood