1. The phone is ringing, it must be Alex. (Это логическое предположение, основанное на факте звонка.)
2. You look sick, you should see a doctor. (Рекомендация, основанная на наблюдении.)
3. They don't have to drink coffee if they prefer tea. (Отсутствие необходимости, выбор.)
4. Somebody was calling last night, but I couldn't answer, I was asleep. (Невозможность действия из-за обстоятельств.)
5. She can't come to the meeting, she is out of the country now. (Физическая невозможность.)
6. Be careful. You must not/should not use your cell phone when you are driving. (Запрет или сильная рекомендация не делать что-либо.)
7. You could/might spend the day watching TV. Go and do something more productive. (Предложение или возможность, но с намеком на то, что это не лучший вариант.)
8. A: Do you know who's that girl sitting next to Sam? B: I have no idea but it could/might be his girlfriend. (Предположение о возможности.)
9. May/Can I use your laptop for an hour? (Просьба о разрешении.)
10. Karla can sing really well but she cannot/can't play any musical instrument. (Констатация факта отсутствия навыка.)
11. My father could fly a plane when he was younger. (Способность в прошлом.)
12. We must buy the ticket now if we want to watch the soccer match. (Необходимость действия для достижения цели.)
13. If you are planning to travel you must/will need to have a passport. (Строгая необходимость.)
14. Buy a lottery ticket. You might/could be lucky. (Возможность.)
15. Paula couldn't/wasn't able to go to the meeting last week. She was ill. (Невозможность действия в прошлом из-за обстоятельств.)