Study materials
To avoid repeating a word or a whole idea, English puts a short word in its place.
I need a pen. Have you got one?
Will it rain? I think so.
This article explains one and ones in place of a countable noun, so and not in place of a whole idea after think, hope or be afraid, and why people do not say I don't hope so or I know so.
One and ones
To avoid repeating a countable noun, one that has a plural, use one for the singular and ones for the plural.
I need a pen. Have you got one?
Which shoes? The blue ones.
This cake is nice, but I prefer the one Granny makes.
With uncountable words, like water, coffee or advice, one is not used. Some or any is used, or nothing: I need water. Have you got any?
So and not for an idea
After think, hope, suppose, guess, expect and be afraid, so replaces a whole positive clause, and not a negative one.
Will it rain? I think so.
Is he coming? I hope not.
Did we lose? I'm afraid so.
Unfortunately, yes.
The negative is built differently. After think, suppose and expect people usually say I don't think so. After hope and be afraid only I hope not and I'm afraid not are used. I don't hope so is wrong.
Common mistakes
The first mistake is one in place of an uncountable noun.
I need water. Have you got one? → Have you got any?
Water is not counted.
The second mistake is negating hope.
Will it rain? I don't hope so. → I hope not.
Hope takes only not.
The third mistake is so after know.
Is the shop open? I know so. → Yes, I know it is.
Know does not take so.
The first mistake shows in the noun itself. Water, advice and money are not counted, so one cannot replace them, and some or any is used. The second shows after hope and be afraid. They take only not. The third shows after know. Know does not take so, people simply say I know.