There are a number of ways to record multiple event probabilities, you can use for example probability trees, sample space diagrams or two way tables.
Today, we'll look at another type of diagram that can be used to record the outcomes for two or more events. Frequency trees.
Frequency trees are just used to classify information. Let's look at a couple to illustrate this point.
Example 1:
60 people are members of a gym. Of these 45 are male.
Draw a frequency tree to show this information.
We can see here that there is only 1 piece of information (the gender) so we only need a one branch frequency tree. Each 'branch' of the tree will have one of the options.
We can now start building our tree. We know that there are 60 people in total, so we place this information in the first space.
We also know that we have 45 males.
Which means we must have 15 females.
Example 2: In a class of 32 students, 18 are boys of which 7 are left handed.
There are 15 left handed people in the class all together.
If I pick a student at random, what is the probability it is a right handed girl.
We can see there are 2 options here, Gender and left handed/right handed. This means we need a two level frequency tree,
Once we have the structure. We can start working out what goes where.
We have 32 students, if 18 are male, this means 14 must be female,
We are told that 7 of the boys are left handed so 11 of the boys must be right handed
We are also told that there are 15 left handed people alltogether, if 7 boys are left handed then 8 girls must be
This leaves us with 6 right handed girls.
We can now finally answer our probability question.
We know we have 6 right handed girls out of the 32 students which gives a probability of...

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