- A-Level Maths

# Probability

**Probability** is used to predict the likeliness of something happening. It is always given between 0 and 1.

An

**experiment**is a repeatable process that can have a number of outcomesAn

**event**is one single or multiple outcomesA

**sample space**is the set of all possible outcomes

For two events, E₁ and E₂, with probabilities P₁ and P₂ respectively:

To find the probability of

**either E₁ or E₂**happening,**add**the two probabilities, P = P₁ + P₂To find the probability of

**both E₁ and E₂**happening,**multiply**the two probabilities, P = P₁ x P₂

The sample space for rolling two fair six-sided dice and adding up the numbers that show would look like this:

To work out the probability of getting a particular result, you count how many times the result occurs and divide by the total number, 36 (since 6² = 36). So to work out the probability of getting a 10, count the number of tens and divide by 36: 3/36 = 0.0833

Generally, give your answers as decimals to three significant figures

## Conditional Probability

If the probability of an event is dependent on the outcome of the previous event, it is called **conditional**. Conditional probability is noted using a vertical line between the events:

The probability of B occurring, given that A has already occurred is given by P(B|A)

For two **independent events:**

P(A|B) = P(A|B') = P(A)

Experiments with conditional probability can be calculated using a **two-way table**/restricted sample space:

## Venn Diagrams

A **Venn diagram** is used to represent events happen