- Define and explain Probability scale and basics in your own words
- Use key terms such as Probability accurately
- Apply what you have learned to new examples and questions
- Avoid the common mistakes learners make with this topic
Probability puts a number on uncertainty. From games of chance to weather forecasts, it lets you calculate exactly how likely an outcome is — and avoid being fooled by gut instinct.
This lesson focuses on Probability scale and basics: the 0 to 1 scale, equally likely outcomes, and writing probabilities as fractions, decimals or percentages.
The 0 to 1 scale, equally likely outcomes, and writing probabilities as fractions, decimals or percentages.
Key ideas
Tree diagrams
A tree diagram shows every branch of a multi-step experiment with probabilities on each branch. Multiply along a branch for that route's probability; add the routes that satisfy the event. Always check all branches from one point sum to 1.
The addition rule
For mutually exclusive events, P(A or B) = P(A) + P(B). Rolling a 1 or a 6 on a fair die gives 1/6 + 1/6 = 2/6 = 1/3. This only works when the events cannot both happen.
Key term — Probability: A number between 0 and 1 measuring how likely an event is, where 0 means impossible and 1 means certain. For equally likely outcomes it is (favourable outcomes) ÷ (total outcomes).
A spinner has sectors 1, 2, 3, 4 (equally likely). Find P(spinning a 1 or a 2).
P = 1/4 + 1/4 = 1/2.
Answer: P = 1/4 + 1/4 = 1/2.
- Adding probabilities of events that overlap The addition rule needs mutually exclusive events; drawing a red card or a king double-counts the king of hearts.
- Forgetting all branches must sum to 1 From any point on a tree, the branch probabilities must total 1; a different sum means a branch is wrong or missing.
Practice
P = 3/6 = 1/2.
P = 1/2 × 1/2 = 1/4.
P = 1 − 0.3 = 0.7.
P = 4/10 = 2/5.
Quick check
Which of these best defines "Probability"?
Two dice are rolled. Find P(total of 7).
- Probability scale and basics: the 0 to 1 scale, equally likely outcomes, and writing probabilities as fractions, decimals or percentages.
- Tree diagrams: A tree diagram shows every branch of a multi-step experiment with probabilities on each branch.
- Mutually exclusive: Two events that cannot happen at the same time, such as rolling a 2 and rolling a 5 on one throw; their probabilities add.
- Watch out for: adding probabilities of events that overlap