Probability Diagrams and Formal Independent/Conditional Notation
Probability has its own diagrams and its own shorthand. Learn to read sample space diagrams, tree diagrams and Venn diagrams, and to use the formal notation for complement, independent, mutually exclusive and conditional events.
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The language of chance 🎲
Probability comes with its own **diagrams** and its own **shorthand**. Master both and long questions become quick. This module covers the diagrams - sample space diagrams, tree diagrams and Venn diagrams - and the **formal notation** for the complement, independent, mutually exclusive and conditional events. (Symbols shown here are standard exam notation.)
The words you need 🔑
Four ideas run through the whole topic.
Match each symbol to its meaning 🔗
- P(A')
- P(A ∩ B)
- P(A ∪ B)
- P(A | B)
- The probability that A does NOT happen
- The probability that both A and B happen
- The probability that A or B (or both) happens
- The probability of A given that B has happened
Independent events ✖️
For two independent events A and B, what is P(A and B)?
- P(A) multiplied by P(B)
- P(A) plus P(B)
- P(A) minus P(B)
- P(A) divided by P(B)
Three rules to know 📋
Almost every probability calculation uses one of these: - **Independent events**: P(A ∩ B) = P(A) x P(B) (multiply) - **Mutually exclusive events**: P(A ∪ B) = P(A) + P(B) (add) - **Conditional probability**: P(A | B) = P(A ∩ B) / P(B) (divide) Choosing the right rule is the whole skill: multiply for independent "and", add for mutually exclusive "or", divide for "given".
Both heads 🪙
An interactive activity.
Two ideas people mix up ⚖️
Independent and mutually exclusive are NOT the same thing - and they use different rules.
Match each diagram to what it shows 🌳
- Sample space diagram
- Two-way table
- Tree diagram
- Venn diagram
- A grid of all possible outcomes of two events
- Frequencies split across two categories at once
- Branches showing outcomes and probabilities in stages
- Overlapping circles showing what sets share
Which show probability? ✅
Select the TWO diagrams used to represent probability in this topic.
- Tree diagram
- Venn diagram
- Pie chart
- Histogram
It might rain 🌧️
An interactive activity.
The notation in words 🧩
In probability notation, P(A') means the _____ of A, found as 1 - P(A). P(A ∩ B) is read 'A _____ B'. If two events are _____, then P(A ∩ B) = P(A) x P(B). If two events are mutually _____, they cannot both happen. P(A | B) is a _____ probability.
Given that... 🔢
An interactive activity.
Pick the right rule 🎬
An interactive activity.
The grade-9 habit 🌟
Winning marks here is about **choosing the right rule**: **multiply** for independent "and", **add** for mutually exclusive "or", and **divide** for a conditional "given". Keep two traps in mind: the **complement** is 1 - P(A), and **mutually exclusive** (cannot both happen) is NOT the same as **independent** (one does not affect the other). Read the words, pick the rule, then calculate.