Probability Basics
Discover how to describe and calculate the likelihood of events using sample spaces, equally likely outcomes and fractions.
What is Probability?
Probability measures how likely it is that an event will occur. It is always a number between 0 and 1:
🙅
Impossible
P = 0
Rolling a 7 on a standard die
🤔
Even Chance
P = ½
Flipping heads on a fair coin
😁
Certain
P = 1
Rolling less than 7 on a die
Sample Space & Probability Formula
The sample space is the set of ALL possible outcomes of an experiment. We list it using curly brackets { }.
Example: Rolling a standard six-sided die
Sample space = {1, 2, 3, 4, 5, 6}
Total outcomes = 6
Probability Formula
P(event) = number of favourable outcomes⁄total number of equally likely outcomes
Example: P(rolling a 4) = 1⁄6
Example: P(rolling an even number) = 3⁄6 = 1⁄2
Complementary Events
The complement of an event A is everything that is NOT A. The probabilities of an event and its complement always add to 1.
P(A) + P(not A) = 1
So: P(not A) = 1 − P(A)
Example:
If P(it rains tomorrow) = 0.3, then P(it does NOT rain) = 1 − 0.3 = 0.7
Key Vocabulary
Probability
A number between 0 and 1 that describes how likely an event is to occur. Can be written as a fraction, decimal or percentage.
Sample Space
The complete list of all possible outcomes of an experiment. Written in curly brackets, e.g. {H, T}.
Equally Likely Outcomes
Outcomes that have the same chance of occurring. A fair coin has two equally likely outcomes: heads and tails.
Complementary Event
The event that an outcome does NOT happen. P(event) + P(complement) = 1.
Worked Examples
A bag has 3 red, 2 blue and 5 green marbles. Find P(blue).
Total outcomes: 3 + 2 + 5 = 10 marbles
Favourable outcomes: 2 (blue marbles)
P(blue) = 2⁄10 = 1⁄5
A standard die is rolled. Find P(number greater than 4).
Sample space: {1, 2, 3, 4, 5, 6}
Favourable outcomes: {5, 6} = 2 outcomes
P(greater than 4) = 2⁄6 = 1⁄3
P(selecting a vowel from the alphabet) = 5⁄26. Find P(NOT a vowel).
Using complement: P(not a vowel) = 1 − 5⁄26
= 26⁄26 − 5⁄26 = 21⁄26
Knowledge Check
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Key Concepts Summary
- ●Probability is always between 0 (impossible) and 1 (certain).
- ●P(event) = favourable outcomes ÷ total equally likely outcomes.
- ●The sample space lists every possible outcome of an experiment.
- ●Complementary events cover all outcomes: P(A) + P(not A) = 1.
- ●Always simplify probability fractions to their simplest form.