Does anyone know what genre of music is this example: very quiet background music. Also, what instrument is used to make this kind of music? Thanks in advance
Instrument: sounds like a violin, plucked (pizzicato). Example from YT.
The sample is only a few seconds long, hard to determine genre. "Incidental music" as genre, perhaps - could image it ending a scene or linking two scenes.
The sample would be described as a Sting, "short musical phrase, primarily used in broadcasting and films as a form of punctuation" - although you didn't ask this.
These are pizzicato strings, which is what you call an instrument that is usually bowed (violin, cello, viola) being plucked instead. It gives a softer, but more percussive sound than a bowed string. This particular clip sounds like a couple of violins being plucked together.
It's impossible to identify a genre based on only two notes, and pizzicato strings are used in a variety of genres, from classical to jazz to pop, but perhaps you're thinking of something like this song ("Pizzicato Strings"), which is from a subgenre of "easy listening" called "elevator music".