Answer
P(more than 5 years old) $=\frac{17}{24}\approx0.708$
Work Step by Step
The sample space is the caseload. So, N(S) = 24
The event "client is more than 5 years old" = "client is between 6 and 10 years old or between 11 and 14 years old or between 15 and 17 years old". Also, the events "client is between 6 and 10 years old", "client is between 11 and 14 years old" and "client is between 15 and 17 years old" are mutually exclusives.
There are 5 cases involving children between 6 and 10 years old. So, N(6-10) = 5
There are 7 cases involving children between 11 and 14 years old. So, N(11-14) = 7
There are 5 cases involving children between 15 and 17 years old. So, N(15-17) = 5
P(more than 5 years old) = P(6-10) + P(11-14) + P(15-17) =
$\frac{N(6-10)}{N(S)}+\frac{N(11-14)}{N(S)}+\frac{N(15-17)}{N(S)}=\frac{5}{24}+\frac{7}{24}+\frac{5}{24}=\frac{17}{24}\approx0.708$
