Probability Basics - Understanding Chance
Probability tells us how likely something is to happen. It is used in weather forecasts, insurance, games, genetics, and countless other fields. Understanding basic probability gives you a way to reason clearly about uncertainty.
Modern probability theory is usually traced to a series of letters exchanged in 1654 between two French mathematicians, Blaise Pascal and Pierre de Fermat, who were asked by a gambler named the Chevalier de Méré to solve a dispute about how to fairly divide the stakes of an interrupted dice game – a puzzle known as the “problem of points.” Their correspondence laid the mathematical foundations for reasoning rigorously about chance for the first time. That foundation now underpins an entire industry: insurance companies employ actuaries whose whole job is calculating the probability of events like accidents, illness, or death, so that premiums can be set precisely high enough to cover expected payouts while still making a profit.
The Probability Scale
Probability is always a number between 0 and 1 (inclusive).
0 = impossible (will never happen).
1 = certain (will definitely happen).
Values in between describe varying degrees of likelihood.
| Word | Meaning | Approx. value |
|---|---|---|
| Impossible | Cannot happen | 0 |
| Unlikely | Less than even chance | 0 < P < 0.5 |
| Even chance | Equally likely or not | 0.5 |
| Likely | More than even chance | 0.5 < P < 1 |
| Certain | Will definitely happen | 1 |
The Probability Formula
P(event) = Number of favourable outcomes ÷ Total number of equally likely outcomes
Worked Examples
Favourable outcomes = 1 (the face showing 4). Total outcomes = 6. P(4) = 1/6 ≈ 0.167.
Total counters = 3 + 5 + 2 = 10. Blue = 5. P(blue) = 5/10 = 1/2.
Hearts = 13. Total = 52. P(heart) = 13/52 = 1/4 = 0.25.
Complementary Events
The probability that an event does NOT happen is called the complement.
P(not A) = 1 − P(A)
Example: P(rolling a 4) = 1/6. P(not rolling a 4) = 1 − 1/6 = 5/6.
Expressing Probability
Probability can be written as a fraction, decimal, or percentage. All three are equivalent:
P = 1/4 = 0.25 = 25%.
Key Takeaways
- Probability ranges from 0 (impossible) to 1 (certain).
- P(event) = favourable outcomes ÷ total equally likely outcomes.
- P(not A) = 1 − P(A).
- Probability can be expressed as a fraction, decimal, or percentage.
Practice: Probability
You Have Completed the Data Handling and Statistics Section!
Well done – you have worked through all 12 topics in the Data Handling and Statistics section. Return to the Resources page to continue your mathematics journey.