Is it possible for a slow computer to beat the world mining Bitcoin? I've heard it is not profitable to mine bitcoins on a regular computer via CPU anymore. I accept that.

However, if you did install a miner onto a regular computer and that computer randomly generated "guesses" 24/7 (in a non-sequential fashion). Isn't it quite possible that it could make a lucky guess and beat everyone else mining?

Or, is that absolutely impossible?

I'm thinking about trying my luck at this (without joining a pool) (for fun) if it is possible. If impossible, then please explain why.
It is of course possible... however it is incredibly unlikely!

Mining with a CPU has not been profitable since the earliest days of bitcoin, the expected time to find a block is likely on the order of centuries at this point, and by that time you'll have burned much more in electricity costs than the eventual block reward.

So, as an experiment you could try, but if it costs you even just $5 worth of electricity a month, you would actually have better odds spending that money on a lottery ticket!