Hi please help.

used to say that one believes that something is true, that a particular situation exists, that something will happen, etc.
"Has she accepted the job?" "I think so."

2
—used to express a positive opinion about a question one has just asked
Is this a good use of our tax dollars? I think so.

What's " I think so" in these two sentence?

Is it equivalent of" yes"?

Question

Hi please help.

used to say that one believes that something is true, that a particular situation exists, that something will happen, etc.
"Has she accepted the job?" "I think so."

2
—used to express a positive opinion about a question one has just asked
Is this a good use of our tax dollars? I think so.

What's " I think so" in these  two sentence?

Is it equivalent of" yes"?

Answer

I think so is less certain than yes. It shows that you think what you say is the truth, but you're short of complete certainty.

You can use I believe so, for example, as an alternative to I think so.

Yes is a positive response that confirms or agrees to something. It is definite.