Probability

This lesson covers probability as required by the Edexcel A-Level Mathematics specification (9MA0), Paper 3 Section A -- Statistics. You need to understand Venn diagrams, tree diagrams, conditional probability using the formula P(A|B) = P(A and B) / P(B), and the concepts of mutually exclusive and independent events.

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Basic Probability Rules

The probability scale

• All probabilities lie between 0 and 1 (inclusive): 0 ≤ P(A) ≤ 1.
• P(A) = 0 means event A is impossible.
• P(A) = 1 means event A is certain.
• P(A') = 1 - P(A), where A' is the complement of A (i.e. A does not occur).

The addition rule

For any two events A and B:

P(A or B) = P(A) + P(B) - P(A and B)

Exam Tip: The subtraction of P(A and B) avoids double-counting the outcomes where both A and B occur.

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Venn Diagrams

A Venn diagram uses circles inside a rectangle to represent events and their probabilities.

Setting up a Venn diagram