I am an occasional teacher.
Here is my question:
Does the word "random" have a technical meaning in mathematics?

Hi Hugh,
The word random appears many places in mathematics and statistics, but as far as I know as an adjective. There are random variables, random samples, random processes and perhaps more. In each case there is some chance or uncertainty involved.
  If you have 10 donuts in front of you and you are to select a "random sample" of size 3 then you need a process to select the sample so that any sample of size 3 is as likely to be selected as any other.
  A "random process" is some experiment or process that involves uncertainty. For example toss a coin. This is a random process since there is chance involved and the result is not predictable with certainty.
  A "random variable" is a number that results from a random process. Here you might toss two dice and total the numbers that appear on the tops of the dice. Perhaps a better example is the type of random variables that pollsters report. Select a random sample of 1 000 people, ask each of them if they are in favour of capital punishment, and report the percentage who say yes. This percentage is a random variable since it depends on the particular sample selected.
  I am not aware of a technical meaning for the word random except to say that is an adjective used when there is chance or uncertainty involved.

Cheers
Harley