2.1StatisticsCore

Set Notation

Set notation gives a precise language for probability. Union, intersection and complement describe how events combine, and they map directly onto regions of a Venn diagram.

22 min Conditional Probability

Edexcel A level Maths: 2.1 Set NotationCurated by Kepler, not produced by us. Watch it before the notes below.

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What you'll be able to do

Use ∪, ∩ and complement notation
Translate between words and symbols
Relate notation to Venn diagram regions
Express probabilities using set notation

The symbols

$A \cup B$ is “ $A$ or $B$ ” (union). $A \cap B$ is “ $A$ and $B$ ” (intersection). $A'$ is “not $A$ ” (complement). $P(A') = 1 - P(A)$ .

A \cup B \ (\text{or}), \quad A \cap B \ (\text{and}), \quad A' \ (\text{not})

Core set operations.

Example 1If

P(A) = 0.3

, find

P(A')

P(A') = 1 - P(A)

= 1 - 0.3 = 0.7

Answer

0.7

Tip — ∪ looks like a U for “Union/or”; ∩ is the cap for “and”.

Venn diagram regions

Each set expression shades a region: $A \cap B$ is the overlap, $A \cup B$ is everything in either circle, $A'$ is everything outside $A$ .

Formula recap

A \cup B = A \text{ or } B

Union.

A \cap B = A \text{ and } B

Intersection.

P(A') = 1 - P(A)

Complement.

Common mistakes to avoid

Swapping ∪ and ∩.

∪ = or (union); ∩ = and (intersection).

Writing P(A′) = −P(A).

P(A′) = 1 − P(A).

Key takeaways

∪ = or, ∩ = and, A′ = not.
P(A′) = 1 − P(A).
Set expressions correspond to Venn diagram regions.

Test yourself

Answer a few questions, then review anything you missed.

Prefer paper? Open the written self-check

Answer each question before opening its answer. This self-check does not record a quiz score.

$A \cap B$ means:
- A and B
- A or B
- not A
- A given B
Show answer and explanation
Answer: A and B
Intersection.
$A \cup B$ means:
- A or B
- A and B
- not A
- A given B
Show answer and explanation
Answer: A or B
Union.
If $P(A) = 0.3$ , then $P(A')$ is:
- $0.7$
- $0.3$
- $-0.3$
- $1$
Show answer and explanation
Answer: $0.7$
1 − 0.3.
$A'$ on a Venn diagram is:
- everything outside A
- the overlap
- inside A only
- the whole diagram
Show answer and explanation
Answer: everything outside A
Complement.
The overlap of two circles represents:
- $A \cap B$
- $A \cup B$
- $A'$
- $B'$
Show answer and explanation
Answer: $A \cap B$
Both events.

Next step

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