Relative frequency
Relative frequencies give an indication of how often an event might occur. Relative frequencies can be shown as fractions, decimals or percentages.
Example 100 teenagers were asked what their favourite flavour out of five types of icecream was and the results were recorded in a frequency table.
The relative frequency is the FRACTION or PROPORTION of people in that particular category.
e.g. 20 out of the 100 teenagers liked strawberry icecream so the relative frequency of strawberry icecream being chosen is 20/100 = 0.2 = 20%
Notice that the relative frequencies always add up to 1 or 100%.
Based on these results it is more likely that the next person asked would like chocolate icecream as it has the highest relative frequency.
How likely an event is to happen can be predicted by its relative frequency.
Relative frequency

Likelihood of event happening

Above 90%

Very likely to happen

Above 50%

Likely to happen

Below 50%

Unlikely to happen

Below 10%

Very unlikely to happen

Relative frequencies are usually the result of an experiment or survey.
Probability
Probabilities give an indication of the chance that an event will happen. Probabilities can be expressed as fractions, decimal fractions or percentages.
The probability of an event happening =
Some examples:
Event 1 
Probability 
That a head will be face up, when a coin is tossed .

1/2 or 50% or 0.5

Event 2 
Probability 
That a 2 will be face up when a dice is thrown.

1/6 or 16.7% or 0.17

Event 3

Probability

That the first ball to come out in a Lotto draw is number 22. (There are 40 balls.) 
1/40 or 2.5% or 0.025 
The lowest probability is 0.
If the probability of an event happening is 0, the event cannot occur.
e.g. P( throwing a sixsided die and scoring a 7) = 0

The highest probability is 1.
If the probability of an event happening is 1, the event is certain to occur.
e.g P( throwing a sixsided die and scoring less than 7) = 1

Tree Diagrams
A tree diagram can help to solve probability problems or problems involving the number of ways that things can be carried out.
e.g. A car can be bought in two colours, blue and red. Each car can be bought with or without air conditioning. How many different combinations can be chosen?
A tree diagram helps solve this problem.
There are four possible combinations available to the car buyer.
Probabilities and Tree Diagrams
If the probabilities of the events on a tree diagram are known, then the probability of each combination occuring can be calculated.
If there were 6 blue cars and 4 red cars, and the probability of any car having air conditioning was 0.5, then the following additions could be made to the diagram.
Notice that the fractions on each pair of "branches" always add up to 1.
From this diagram the probability of each combination being chosen can be calculated.
Combination

Probability

blue with air conditioning


blue without air conditioning


red with air conditioning


red without air conditioning


Notice that because all of the combinations are covered the probabilities add up to 1.
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