What Is Probability?
Before we dive into complementary events, let's make sure we're solid on what probability actually means.
A measure of how likely an event is to occur, expressed as a number between 0 and 1 (or as a percentage between 0% and 100%).
- A probability of 0 means the event is impossible (it will never happen).
- A probability of 1 means the event is certain (it will definitely happen).
- A probability of 0.5 (or 50%) means the event is equally likely to happen or not happen.
Think of probability like a volume dial that goes from 0 to 1. At 0, the music is completely off (impossible). At 1, it's at full blast (certain). Most events sit somewhere in between.
We can write probability as a fraction, a decimal, or a percentage. For example, the probability of flipping heads on a fair coin is:
Theoretical Probability
The probability of an event calculated by reasoning about all equally likely outcomes, without actually performing an experiment. It is found using the formula:
Theoretical probability is what we expect to happen based on logic and mathematics. We don't need to roll a single die or flip a single coin — we just think it through.
Example: Rolling a standard 6-sided die
What is the theoretical probability of rolling a number greater than 4?
Step 1: Identify all possible outcomes: {1, 2, 3, 4, 5, 6} → 6 outcomes total
Step 2: Identify favourable outcomes (greater than 4): {5, 6} → 2 favourable outcomes
Step 3: Apply the formula:
Theoretical probability assumes that all outcomes are equally likely. A fair coin has equal chances of heads and tails. A fair die has equal chances of landing on any face. If the outcomes aren't equally likely (like a weighted die), theoretical probability becomes more complicated.
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