# Probability

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• Created on: 05-06-11 16:12

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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 you 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
There are two main types of event:
1. Mutually exclusive events
Mutually exclusive events are events which cannot happen at the same time
i.e. 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)

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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.…read more