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.
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 Questions
- A bag has 4 red, 6 blue, and 10 green balls. Find P(red), P(blue), and P(green).
- A spinner has 8 equal sections numbered 1 to 8. Find P(even number).
- A fair coin is flipped. Find P(heads) and P(not heads).
- A class has 18 girls and 12 boys. One student is chosen at random. Find P(boy).
- P(winning a prize) = 0.15. Find P(not winning a prize). Express as a percentage.
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.