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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:

Sample space diagram, how to draw a sample space, what is a sample space, probability, statistics. Free online a-level maths notes. EngineeringNotes.net, EngineeringNotes, Engineering Notes.

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:

Conditional probability conditional probability example, how to work out conditional probability. probability, statistics. Free online a-level maths notes. EngineeringNotes.net, EngineeringNotes, Engineering Notes.



Venn Diagrams

A Venn diagram is used to represent events happen