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• 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 outcomes

• An event is one single or multiple outcomes

• A 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 + P₂

• To 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

## 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