can vs may

a) Posibilidad vs Probabilidad
"Can" indica que algo es posible (las circunstancias lo permiten o alguien tiene la habilidad de hacerlo).

I can play tennis quite well
I can open that door with my key
I can run for two hours
This car can go faster than 200 km per hour
You can go to France without a passport

"May" indica que algo es probable; equivale a "perhaps"

My friend may win the race
The sky is very dark. It may rain