Assume is used when there is reasonable hypothesis based on evidence. For example, if we go to someone's house and see a stethoscope, we assume that there may be a doctor in this house.
Presume is used when we lack evidence and the hypothesis is more open to questions. For example, suppose there is an emergency in train and there is a need of doctor. Here we don't have any evidence of a person being a doctor but we presume that in such a big train there might be some doctor and if we try to find out we might succeed.
Sample Usage
Assume:
1. Because I see you dressed in a school dress, I assume you are going to school.
2. As I see a bag in your hand, I assume you have bought vegetables!
3. I can see your eyes red, I assume you slept late last night.
Presume:
1. I do not know you at all, but I presume you are a good person.
2. I have never done this task ever before, but I presume it would be easy.
3. I have never seen her, but I presume she is beautiful.
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