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For some songs and musical pieces that I am listening to for the first time, why is it that I can occasionally guess what the next note will be? I imagine the next note in my head and sometimes it is exactly correct.

I find that this happens more often for slow piano pieces - but occasionally for other kinds of music. Is there some kind of musical theory that somewhat determines what the next note can/should be to make the piece sound good?

And sometimes I also imagine two possible notes, and one of them is correct.

I play the drums and guitar but I'm not very good, and I have limited musical knowledge outside of those instruments. So it's quite an odd experience for me.

First off, for any melody that stays within a key, you have about a 1/7 chance of any random note you guess being the next note.

Second, there are popular melody patterns and techniques, and sometimes the chords being played will suggest likely places for the melody to go. Depending on the chords and the harmony, you may be instinctively understanding that a chord tone is likely, and that brings the probability of a randomly guessed chord tone being right down to 1/3 or 1/4.

This is one way that it's possible for people with no knowledge of music theory to make up their own melodies to hum that sound "good" (at least to them). They are basically guessing what the next note could/should be based on their tonal memory of music that they like and the popular melodic patterns and elements used in that music.

Traditional tonal music plays with expectations.

Music can do many surprising and unexpected things, but very often music will do what is "expected" meaning that it follows certain conventions.

Let's switch to a language metaphor just for a moment.

If I say "hello, what is your... ", what word do you expect might be next? Do you think "name?" Certainly you would not expect "rhinoceros", you wouldn't expect "hello" to be repeated. Words like those would be unexpected.

In a similar way music has it's own grammar and syntax, and that grammar and syntax creates expectations for a listener.

So, if I play a V7 chord, it sets up an expectation for a I chord. I may or may not play that I chord, but an expectation is created. You expect to next hear notes from that I chord... and there is a very good chance you will hear them.

Other kinds of expectation can be created. If a melody goes up, eventually it will probably go down. Step-wise movement often continues in one direction. If a melody goes up as DO, RE... there is a reasonable chance that MI will follow. Call and response and other repetition devices also play with musical expectations.

You can’t predict only the next tone. Very often you can even tell or guess a whole phrase.

Melodies are built of motives. This are elements that can be repeated, sequenced or brought back in a inversed form. Music theory and the theory of melody building that describes the structural principles of melodies call it “question and answer” or “response”, “motive and development”:

If you have checked the motiv

do so do sodosodomiso

you can construct e.g. 2 answers:

fa re fa re faretire so

or:

re la re la relarefa la

this can be explained by the inherent logic of a tune
and by principles of the melodic shape (“gestalt”) that are saying e.g.:

The whole is more than the sum of its parts.

Because Common Practice harmony is all about dominants resolving to tonics. About setting up tensions then resolving them. Here's a simplistic example:

You know where that penultimate chord wants to go. Often, you'll be satisfied!