Independent and dependent (note spelling ;) refer to relationships between events. Strictly speaking, only a single event can be neither! But, if you are considering two random events, each event (outcome, in Probability language) was independent of the other. Neither one contributed to causing the other; rather, there was some unknown cause (something we consider random) for each.
Before you leave this topic, you should consider just what could be a random event: is it drawing a particular colored ball from a bag? Really, the balls were put into the bag in a particular order, and then some sort of mechanical process occurred to mix them. If you had extraordinary knowledge about exactly how the balls hit each other and hit the stirrer (let's say), then you might be able to actually predict what color ball you were going to pull out. But for MOST purposes, if the balls were exactly the same weight, slipperiness, and so on, then a little mixing will scramble them adequately.
The same cannot be said for mixing two powdery materials which differ in solid density, particle shape, particle size, tendency to accumulate static electricity on their surface, and so on; in fact, adequate mixing turns out to be quite an art, and it's possible to both undermix or even overmix sometimes! If you become a pharmaceutical chemist or chemical engineer, you will study this sort of thing.
Or, take an expert card-dealer: he/she can mix the deck with one shuffle, then unmix it again on the second shuffle (by exactly controlling how the cards fall, one -by-one, from each side). So the card you eventually get dealt might not be so random as you would hope!
So, it's really a dicey call to call a particular outcome a "random event" -- and an awful lot of the history of science has consisted of making better and better predictions of what once might have been regarded as a random outcome. For instance, some people with a particular medical condition may respond to a certain drug, and others don't. Is this a random outcome? Here, we can frequently detect some physical difference in the biochemistry of individuals that predisposes them to their particular ("idiosyncratic") response to the drug. If you go into medicine or biology, you'll learn a lot about this.
But, certain things happening on a very small size scale ("quantum scale") are, as far as we can experimentally measure and theoretically understand, fundamentally random. The classic example here is the radioactive decay event of an isolated, unstable atom (nucleus). There is no way of knowing how the nucleons are mixing around, such that any useful prediction could be made as to when the nucleus might decay. Not that you couldn't reach in (so to speak) and give them a poke; it's just that the poke would stir them up again, and your measurement could only tell you something about how the nucleus was THEN, which is not necessarily how it is NOW any more!
Hope this not only answers your question, but gives you some ideas for further study on your own (which is something that you should always work towards -- not only do you learn things other people don't, but you might discover some hidden experimental design talents! Go for it!)