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Oversimplification of definitions:

atheist: Believes in no god.

agnostic: that the existence of God, of the divine or the supernatural is unknown or unknowable.

Is there a term for someone who just does not care. Has no opinion about the existence or inexistence of god.

They have simply not looked into it. They have not yet formed an opinion and because of this both terms atheist and agnostic don't seem to fit.

Question: What do I call someone who has not formulated an opinion about god?

https://en.wikipedia.org/wiki/Apatheism

An apatheist is someone who is not interested in accepting or rejecting any claims that gods exist or do not exist. The existence of god(s) is not rejected, but may be designated irrelevant.

Your definition of agnostic is incomplete:

[Merriam-Webster]

1 : a person who holds the view that any ultimate reality (such as God) is unknown and probably unknowable
broadly : one who is not committed to believing in either the existence or the nonexistence of God or a god
2 : a person who is unwilling to commit to an opinion about something

// political agnostics

In all but the strict first sense, an agnostic is simply someone who doesn't believe one way or the other. They think it might be true—or it might not. In other words, they're not committed to any particular viewpoint.

Unless going by that strict first sense of the word, that doesn't mean that they believe something is actually unknowable. In the second sense of the word, and the casual first sense, an agnostic may also have simply not looked into it much or not really care.

Based on that, you have people who are theists, who believe in the existence of something, people who are atheists, who believe in its nonexistence, and people who are agnostics, who don't (or won't) say one way or the other—for whatever reason.

While there's nothing wrong with apatheism in the other answer, people who are agnostics can also be apatheists. And people who are apatheists may well have looked into it carefully and come to a reasoned conclusion (formed an opinion) that the answer doesn't matter. In fact, I'd say that somebody who claims to be an apatheist must already be aware of what that word means, and so would have formed an opinion about God: that it doesn't matter.

In general, somebody who has not formed an opinion at all is simply undecided. And somebody who has never considered something at all is either wilfully or unintentionally ignorant about that thing.