Probability

This lesson covers the fundamental concepts of probability at A-Level, including the rules for combining events, Venn diagrams, and tree diagrams. Probability is the mathematical framework for quantifying uncertainty and forms the basis for all statistical inference.

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Basic Probability Concepts

The probability of an event $A$A is a number between 0 and 1 (inclusive):

$0 \leq P(A) \leq 1$0≤P(A)≤1

Probability	Meaning
$P(A) = 0$P(A)=0	Event $A$A is impossible
$P(A) = 1$P(A)=1	Event $A$A is certain
$P(A) = 0.5$P(A)=0.5	Event $A$A is equally likely to occur or not

The sample space $S$S is the set of all possible outcomes. The complement of $A$A, written $A'$A′, is the event that $A$A does not occur:

$P(A') = 1 - P(A)$P(A′)=1−P(A)

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Venn Diagrams

Venn diagrams are used to visualise events and their relationships. For two events $A$A and $B$B:

• $A \cap B$A∩B — the intersection: both $A$A and $B$B occur.
• $A \cup B$A∪B — the union: $A$A or $B$B (or both) occur.
• $A'$A′ — the complement: $A$A does not occur.

The Addition Rule