may/might

We can use 'may' to ask for permission. However this is rather formal and not used very often in modern spoken English.

• May I leave now?
  
• May I borrow your dictionary?
  
• May we think about it until tomorrow?
  

We use 'may' to suggest something is possible.

• Philip may come to stay with us
  
• I may not have time to do it straightaway.
  
• It may snow later today.
  

might
We use 'might' to suggest a small possibility of something. Often we read that 'might' suggests a smaller possibility that 'may', there is in fact little difference and 'might is more usual than 'may' in spoken English.

• It might rain this afternoon.
  
• She might be at home by now but it's not sure at all.
  
• I might not have time to go to the shops for you.
  
• I might not go.
  

For the past, we use 'might have'.

• He might have tried to call you while you were out.
  
• I might have left it in the taxi.