Possibility is when there is a chance that something may happen or be true while probability is the likelihood of something happening or being true:
"Until yesterday, the project was just a possibility, but now it has become a real probability."
It is likely that it will happen.
- My grandmother may travel alone.
- May be she will make the trip alone.
- Perhaps she will visit London.
- Possibly, she will go by plane.
- It's possible that someone will meet her at the airport.
- She might buy some presents for the family before she goes.
- I suppose she might spend a lot of money on the presents.
- There's a chance she'll like the city.
- She will take an umbrella as it could rain heavily there..
- No, it's impossible to repair that old Chevrolet.
- Even a good mechanic can't possibly fix it.
- We may not be able to travel by car.
- There's no chance my father repairs it tomorrow.