@thesky The difference between I wouldn't and I don't think so is. First wouldn't is the opposite of would. So when you say " I wouldn't think so" what you are saying is just your thought of the matter. And there is room for you to change your mind. When you say "I don't think so" you are stating your absolute thought. And that there is no doubt in your mind about the matter.

The difference is that wouldn't means you do not like to join that but you did it. And the other one you do not like definitely.

"How many miles is Earth from the Sun?" - "I don't know" "What is the weather going to be like tomorrow?" - "I don't know" "How much does your boss earn?" - "I wouldn't know" "When you are rich and famous is it difficult to go to the shops?" - "I wouldn't know"

You're welcome.