Frequency Trees
A frequency tree can be used to record and organise information given as frequencies. This can then be used to calculate probabilities.
Example
A running club has 160 members. 74 of the club members are female. 58 of the female members are over 18. 21 of the male club members are under 18.
Complete the frequency tree to show this information.
Find the The extent to which something is likely to be the case. that a member of the club chosen at random is under 18.
Since 74 members are female, \(160 - 74 = 86\) members must be male.
58 female members are over 18, so \(74 - 58 = 16\) females are under 18.
21 male members are under 18, so \(86 - 21 = 65\) males are over 18.
Adding this information to the frequency tree gives:
The total number of under 18s is \(16 + 21 = 37\), so the probability that a member of the club chosen at random is under 18 is \(\frac {37}{160}\).