Quick answer
Ду́маю, да.
dúmayu da — plus наве́рное, ка́жется and the famous да нет, наве́рное
The options
The scale
From strongest to weakest: то́чно (definitely), скоре́е всего́ (most likely), наве́рное (probably), ка́жется (it seems), мо́жет быть (maybe), вряд ли (unlikely), то́чно нет (definitely not).
The comma
A clause after ду́маю or ка́жется always takes a comma: Ду́маю, что он прав. Russian punctuation is strict here, and the что can be dropped in speech but the comma stays in writing.
да нет, наве́рное
The famous three-word answer: literally “yes no probably”, meaning “no, I don’t think so”. The да is a filler, not an affirmation. It is perfectly normal speech and a good joke to be in on.
What you hear back
Typical mistakes
Я ду́маю да.
Ду́маю, да.
The comma is required, and the я is usually dropped.
Reading да нет as “yes”
It means no
The да is a filler.
Check yourself
What does да нет, наве́рное mean?