I think so means “probably yes”. It's a short answer to a question when you're almost, but not completely, sure. So replaces the whole answer: not I think the shop is open, just I think so.
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I think so; I don't think so; I think so too (= I agree)
- — Did you lock the back door? — I think so, but let me check.
- — Is this the right platform for Leeds? — I don't think so, let's ask someone.
- — This café makes the best coffee in town. — I think so too.
What changed
First version— Is the shop still open? — I think yes, it closes at nine.
Revision— Is the shop still open? — I think so, it closes at nine.
It's tempting to say I think yes. But after think, “yes” is expressed by so. Yes isn't used here.
“Probably not” in conversation is I don't think so: Is it going to rain? — I don't think so. I think not exists, but it sounds formal and abrupt. And I think so too isn't an answer to a question, it's agreement: “I have the same opinion”.
Your turn
— Will Anna come to the meeting? — I ___ so. She's off sick and hasn't replied.
Show the answer
don't think — Anna is ill and hasn't replied, so the speaker expects her not to come. The answer needs to mean “probably not”: I don't think so. I think so would mean she'll probably come.
Write a short dialogue: a friend asks if you'll make the train. Answer I think so and give a reason.
— Will we make the 6:15 train? — I think so, because the taxi is already outside.
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