I think the main disagreement in this thread comes from how people perceive the word "random". Most people understand it to mean something like, "completely decided by chance". That's not the way the word is used in statistics.
A random variable will follow a certain distribution, which can mean that some outcomes are more likely than others. E.g, rolling a pair of dice. Before rolling, you don't know the outcome, but you know you're more likely to roll a 7 than a 2. Just because all outcomes aren't equally likely doesn't mean the variable isn't random.