Do things happen for a reason?

Well yes they do. They do because this is a basic principle of physics. Entropy being the inevitable decline towards inactivity as interaction between physical systems tend inexorably towards equilibreum. In the meantime, physical systems will continue to act upon each other and this is the reason that things happen.

That's not to say there is no random element involved.

I don't believe there's an overarching plan or some kind of guidance for events in the world however. Things happen because they do. Bad things dont happen in order for you to learn from them; bad things happen because the potential for awful is approximately equivalent to the potential for awesome. You grow from negative experience because you siezed an oportunity to better yourself - not because it was some clever lesson concocted by some cosmic/deific intellect to develop you in some way. Positive events are no different, they don't occur because you deserve them. They happen because you created them or the conditions they were dependent on were just so.

Nothing else beyond the infinite possibilites of existence is required to explain this. How you deal with life is a testament to your character and should not be deferred to some ephemeral 'responsible adult' such as fate or God. The interactions of almost seven billion people are more than cause enough for every tragedy and benevolent act ever visited upon one human being by another.