Basic Probability (Cambridge (CIE) IGCSE Maths: Extended): Revision Note
Exam code: 0580 & 0980
Basic probability
What is probability?
Probability describes the likelihood of something happening
In real-life you might use words such as impossible, unlikely and certain
In maths we use the probability scale to describe probability
This means giving it a number between 0 and 1
0 means impossible
Between 0 and 0.5 means unlikely
0.5 means even chance
Between 0.5 and 1 means likely
1 means certain
Probabilities can be given as fractions, decimals or percentages
What key words and terminology are used in probability?
An experiment is an activity that is repeated to produce a set of results
Results can be observed (seen) or recorded
Each repeat is called a trial
An outcome is a possible result of a trial
An event is an outcome (or a collection of outcomes)
For example:
a dice lands on a six
a dice lands on an even number
Events are usually given capital letters
n(A) is the number of possible outcomes from event A
A = a dice lands on an even number (2, 4 or 6)
n(A) = 3
A sample space is the set of all possible outcomes of an experiment
It can be represented as a list or a table
The probability of event A is written P(A)
An event is said to be fair if there is an equal chance of achieving each outcome
If there is not an equal chance, the event is biased
For example, a fair coin has an equal chance of landing on heads or tails
How do I calculate basic probabilities?
If all outcomes are equally likely then the probability for each outcome is the same
The probability for each outcome is
If there are 50 marbles in a bag then the probability of selecting a specific one is
The theoretical probability of an event can be calculated by dividing the number of outcomes of that event by the total number of outcomes
This can be calculated without actually doing the experiment
If there are 50 marbles in a bag and 20 are blue, then the probability of selecting a blue marble is
How do I find missing probabilities?
The probabilities of all the outcomes add up to 1
If you have a table of probabilities with one missing, find it by making them all add up to 1
The complement of event A is the event where A does not happen
This can be thought of as not A
P(event does not happen) = 1 - P(event does happen)
For example, if the probability of rain is 0.3, then the probability of not rain is 1 - 0.3 = 0.7
What are mutually exclusive events?
Two events are mutually exclusive if they cannot both happen at once
When rolling a dice, the events “getting a prime number” and “getting a 6” are mutually exclusive (as 6 is not prime)
If A and B are mutually exclusive events, then the probability of either A or B happening is P(A) + P(B)
Complementary events are mutually exclusive
Examiner Tips and Tricks
If you are not told in the question how to leave your answer, then fractions are best for probabilities.
Worked Example
Emilia is using a spinner that has outcomes and probabilities as shown in the table.
Outcome | Blue | Yellow | Green | Red | Purple |
|---|---|---|---|---|---|
Probability |
| 0.2 | 0.1 |
| 0.4 |
The spinner has an equal chance of landing on blue or red.
(a) Complete the probability table.
Answer:
The probabilities of all the outcomes should add up to 1
1 - 0.2 - 0.1 - 0.4 = 0.3
The probability that it lands on blue or red is 0.3
As the probabilities of blue and red are equal you can halve this to get each probability
0.3 ÷ 2 = 0.15
Now complete the table
Outcome | Blue | Yellow | Green | Red | Purple |
|---|---|---|---|---|---|
Probability | 0.15 | 0.2 | 0.1 | 0.15 | 0.4 |
(b) Find the probability that the spinner lands on green or purple.
Answer:
As the spinner cannot land on green and purple at the same time they are mutually exclusive
This means you can add their probabilities together
0.1 + 0.4 = 0.5
P(Green or Purple) = 0.5
(c) Find the probability that the spinner does not land on yellow.
Answer:
The probability of not landing on yellow is equal to 1 minus the probability of landing on yellow
1 - 0.2 = 0.8
P(Not Yellow) = 0.8
Unlock more, it's free!
Join the 100,000+ Students that ❤️ Save My Exams
the (exam) results speak for themselves:
Was this revision note helpful?
Build on this topic
Questions students ask about Basic Probability
Real questions from students revising this topic on Save My Exams
What are complementary events in probability?
Complementary events are an event and its exact opposite: A happening and A not happening, and one of them must happen, so their probabilities add up to 1.
- The complement of A is the event where A doesn't happen — think of it as "not A".
- The rule is P(event does not happen) = 1 − P(event does happen).
- Complementary events are always mutually exclusive, since A can't both happen and not happen.
Examples (from this page):
- The probability of rain is 0.3, so P(no rain) = 1 − 0.3 = 0.7
- Emilia's spinner lands on yellow with probability 0.2, so P(not yellow) = 1 − 0.2 = 0.8
When to use it: look for the word "not". Subtracting from 1 is usually quicker than adding up all the other outcomes — for the spinner, blue + green + red + purple = 0.15 + 0.1 + 0.15 + 0.4 = 0.8 gives the same answer in four steps instead of one.
What does mutually exclusive mean in probability?
Two events are mutually exclusive if they cannot both happen at the same time.
- Example from this page: when you roll a dice, "getting a prime number" and "getting a 6" are mutually exclusive, because 6 isn't prime — no single roll can be both.
- Adding rule: if A and B are mutually exclusive, P(A or B) = P(A) + P(B).
- Complementary events (A and not A) are always mutually exclusive.
Worked example (from this page): Emilia's spinner lands on green with probability 0.1 and purple with probability 0.4.
- It can't land on green and purple at once, so the events are mutually exclusive.
- Add: 0.1 + 0.4 = 0.5
- P(green or purple) = 0.5
How to check: ask "can one outcome count as both?" If no, you can add. On a dice, "even" and "greater than 3" both include 4 and 6, so they aren't mutually exclusive and adding would count those twice.
When do you use the fraction formula for probability?
Use P(A) = number of outcomes for the event ÷ total number of outcomes whenever every outcome is equally likely — a fair dice, a fair coin, or picking at random from a bag.
Use it when:
- The question says "fair", "at random" or "chosen at random"
- You can count all the outcomes and each has the same chance
Don't use it when:
- The outcomes aren't equally likely (the event is biased) — use the probabilities you're given, remembering they add up to 1
Examples (from this page):
- 50 marbles in a bag, 20 blue: P(blue) = 20/50
- A fair dice landing on an even number: n(A) = 3 (2, 4 and 6) out of 6 outcomes, so P(A) = 3/6
- Emilia's spinner is not equally likely — green is 0.1 but purple is 0.4 — so read the table instead
If the question doesn't say how to give your answer, fractions are best.
