Probability Basics Revision Notes for Edexcel GCSE Maths

Probability basics

Understanding probability might seem challenging at first, but once you grasp the fundamental concepts, it becomes much clearer. Probability helps us measure how likely something is to happen, and it's used everywhere from weather forecasts to games of chance.

The probability scale

All probabilities fall somewhere between 0 and 1, and this scale tells us everything we need to know about how likely an event is to occur.

When we say a probability is 0, this means the event is impossible and will never happen. At the other end, a probability of 1 means the event is certain and will definitely happen. Everything else falls somewhere in between these two extremes.

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Understanding the Probability Scale

The scale works like this:

0: Impossible - will never happen
0.25 (or ¼): Not very likely
0.5 (or ½): As likely as not (50-50 chance)
0.75 (or ¾): Very likely
1: Certain - will definitely happen

Remember that probabilities can be expressed as either fractions or decimals, and both are equally valid ways to show the same information.

Basic probability formula

When all possible outcomes are equally likely, we can calculate probability using a straightforward formula.

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Key Formula for Equally Likely Outcomes

$\text{Probability} = \frac{\text{Number of ways for something to happen}}{\text{Total number of possible results}}$

This formula only works when every possible outcome has an equal chance of occurring. Words like "fair" or "at random" in questions usually indicate that all outcomes are equally likely.

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Worked Example: Selecting Letter Tiles

If you're randomly selecting a letter from the tiles A-P-P-L-E-P-I-E:

There are 3 letter P's out of 8 total tiles
So the probability of picking a P = $\frac{3}{8}$ (or 0.375)

This approach works because each tile has an equal chance of being selected.

Probabilities add up to 1

One of the most important rules in probability is that when you consider all possible outcomes together, their probabilities must total exactly 1.

This happens because something must definitely happen when you perform an action - one of the possible outcomes will occur. Since the probability of "something happening" is 1 (certain), all the individual probabilities must add up to this total.

Colur	red	blue	yellow	green
Probablity	0.1	0.4	0.3

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The Addition Rule

$\text{All probabilities in a complete set} = 1$

This rule is particularly useful when you know some probabilities but need to find others.

In the spinner example, if you know the probabilities for red (0.1), blue (0.4), and yellow (0.3), you can find the probability for green by subtracting from 1:

$P(\text{green}) = 1 - (0.1 + 0.4 + 0.3) = 1 - 0.8 = 0.2$

Working with complementary events

Complementary events are pairs of outcomes where one or the other must happen, but not both. The most common example is that something either happens or it doesn't happen.

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Complementary Events Formula

$P(\text{event happens}) + P(\text{event doesn't happen}) = 1$

This relationship is incredibly useful for solving problems.

If you know the probability of something happening, you can immediately find the probability of it not happening by subtracting from 1.

For instance, if the probability of rain tomorrow is 0.3, then the probability of no rain is $1 - 0.3 = 0.7$ .

Solving probability problems

When approaching probability questions, a systematic approach will help you avoid common mistakes and arrive at the correct answer.

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Step-by-Step Problem Solving

Identify what type of problem it is: Are all outcomes equally likely? Are you looking for complementary probabilities?
Count carefully: Make sure you count all favourable outcomes and all possible outcomes correctly.
Apply the right method: Use the basic formula for equally likely outcomes, or use the addition rule for complementary events.
Check your answer: Does your probability fall between 0 and 1? Do all probabilities in the problem add up to 1?

Remember!

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Key Points to Remember:

All probabilities must be between 0 and 1, where 0 means impossible and 1 means certain
The basic formula (favourable outcomes ÷ total outcomes) only works when all outcomes are equally likely
In any complete set of outcomes, all probabilities must add up to exactly 1
If you know some probabilities in a complete set, you can find the missing ones by subtracting from 1
Complementary events (like "happens" and "doesn't happen") always have probabilities that sum to 1

Probability Basics (Edexcel GCSE Maths): Revision Notes