Probability Basics Revision Notes for AQA GCSE Maths

Probability basics

Many students find probability challenging at first, but once you understand the fundamental concepts, it becomes much clearer. Probability is essentially about measuring how likely something is to happen, and there are some key principles that will help you solve any probability question.

Understanding the probability scale

The most important thing to remember is that all probabilities fall between 0 and 1. Think of this as a scale where:

0 (Impossible): Something that can never happen
1/4 (Unlikely): Something that probably won't happen but could
1/2 (Evens): Something that has an equal chance of happening or not
3/4 (Likely): Something that will probably happen
1 (Certain): Something that will definitely happen

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Understanding this scale is crucial for developing probability intuition. Every probability value you calculate should fall somewhere on this continuum from impossible to certain.

What's really useful is that probabilities can be expressed in three different ways, and you should be comfortable converting between them:

Fractions: $\frac{1}{4}$ , $\frac{1}{2}$ , $\frac{3}{4}$
Decimals: 0.25, 0.5, 0.75
Percentages: 25%, 50%, 75%

The higher the probability value, the more likely something is to occur. A probability of 0.9 means something is very likely to happen, while a probability of 0.1 means it's quite unlikely.

Calculating probability using the formula

When all possible outcomes are equally likely, you can use a simple formula to calculate probability:

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Probability = Number of favourable outcomes ÷ Total number of possible outcomes

This formula is your best friend, but remember it only works when each outcome has the same chance of occurring.

Words like "fair", "unbiased", and "random" in questions usually indicate that outcomes are equally likely.

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Worked Example: Letter Tiles

Imagine you have letter tiles spelling "APPLE PIE" and you pick one letter at random. Find the probability of picking the letter 'P'.

Step 1: Count the favourable outcomes There are 3 tiles with 'P' on them.

Step 2: Count the total possible outcomes
There are 8 tiles altogether.

Step 3: Apply the formula Probability = $\frac{3}{8}$ (or 0.375 as a decimal)

This systematic approach works for any equally likely situation - just identify your favourable outcomes and total possible outcomes.

The fundamental rule: probabilities add up to 1

Here's a crucial concept that will help you check your work and solve many problems: when you consider all possible outcomes for a situation, their probabilities must add up to exactly 1.

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P(event happening) + P(event not happening) = 1

This happens because something must happen - one of the possible outcomes will definitely occur.

You can rearrange this to find missing probabilities:

P(event happening) = 1 - P(event not happening)
P(event not happening) = 1 - P(event happening)

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Worked Example: Spinner Probabilities

A spinner has sections coloured red, blue, and green with probabilities 3x, 2x, and 5x respectively. Find the individual probabilities and P(red or blue).

Step 1: Use the fact that all probabilities sum to 1 $3x + 2x + 5x = 1$ $10x = 1$ $x = 0.1$

Step 2: Calculate individual probabilities

Red = $3x = 3(0.1) = 0.3$
Blue = $2x = 2(0.1) = 0.2$
Green = $5x = 5(0.1) = 0.5$

Step 3: Find P(red or blue) Method 1: Add probabilities = $0.3 + 0.2 = 0.5$ Method 2: Use complement = $1 - P(\text{green}) = 1 - 0.5 = 0.5$

This complementary approach is particularly useful when it's easier to calculate the probability of something not happening rather than it happening.

Practical tips for success

When approaching probability questions, always start by identifying what type of situation you're dealing with.

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Key Questions to Ask Yourself:

Are all outcomes equally likely?
What exactly am I being asked to find?
Can I use the complement to make the calculation easier?

Remember that probability questions often involve careful reading. Make sure you understand whether you're looking for "and", "or", or "not" - these small words make a big difference to your calculation approach.

For more complex problems, drawing a simple diagram or listing all possible outcomes can help you visualise the situation and avoid mistakes.

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Key Points to Remember:

All probabilities are between 0 and 1 - anything outside this range means you've made an error
The probability formula only works when all outcomes are equally likely
Probabilities can be expressed as fractions, decimals, or percentages
All possible outcomes for a situation must add up to a probability of 1
Use complements (P(not A) = 1 - P(A)) to make calculations easier when appropriate

Probability Basics (AQA GCSE Maths): Revision Notes