**Probability**

- Probability involves the study of the laws of chance and is a measure of the likelihood of an event happening.
- Rather than use words to describe the chance of an event happening, we can give probability as a number, usually written as a fraction or decimal,
**between 0 and 1**. - If it is impossible for an event to happen then the probability is 0.
- If an event is certain to happen then the probability is 1.
- All other probabilities are greater than 0 but less than 1.
- Sometimes probabilities are written as percentages, between 0 and 100%.
- To compare probabilities you must compare the relative sizes of the fractions, decimals or percentages.

**Listing Outcomes**

- Consider a six sided die, on one throw of the die you can have 1 of 6 possible outcomes i.e. 1,2,3,4,5,6.
- If you want to find the event “The number on the die is an even number” then you would be interested in the numbers 2,4,6 . These numbers are said to be favourable outcomes.

**Calculating Probabilities **

- If, in an experiment each outcome is as likely to occur as any other outcome then you have what are called equally likely outcomes.
- It is possible to calculate the probability of an event happening using the following formula:

Probability of an event happening = **(Number of favourable outcomes) / (Total number of outcomes)**

When it comes to IGCSE/GCSE Maths, do you remember how to calculate the probability of the two main types of events?

**Mutually Exclusive Events**

Mutually exclusive events are events which cannot happen at the same time.

If you roll a die the outcome will be a score of 1,2,3,4,5,6 but only one of these can occur, for example, the score 2 and 3 cannot occur at the same time.

For any two mutually exclusive events A and B:

**P(A or B) = P(A)+P(B)**

The probability of an event not happening can be expressed thus: P(event does not happen) = 1- P(event happens)

**Independent Events**

- Independent events are events, which do not affect each other e.g. tossing a coin and throwing a die.

To find the probability that two independent events will happen we multiply their respective probabilities:

**P(A and B) = P(A) * P(B)**

**Tree Diagrams**

- Listing outcomes can be a very hazardous job.
- A tree diagram is another way of listing outcomes and helps to simplify the calculation of probabilities when combined events are concerned.
- Each ‘branch’ of the tree indicates the outcome at each stage.
- Each route along the tree leads to a combined event.
- The tree is usually created across the page but can be drawn down the page.
- Consider a coin being tossed three times, the diagram below represents the possible outcomes, where H denotes a head and T a tail.

That's the end of the topic!

Drafted by Bonnie (Mathematics)