Modals of probability/possibility (Deduction)

What modal verb do we use when we are SURE that something is true (even though we don't actually know)?

He ______ be his son, they look completely different.

If you haven't eaten all day, you ________ be hungry.

David __________ be happy. His girlfriend has just broken up with him.

David really likes that restaurant. He _______ be there now.

Sarah always does really well on exams. She ________ study a lot.

It ____ be raining outside. All the students brought an umbrella.

It ________ be hot outside. That man in the street is wearing a coat.

What modal verbs do we use when we are think something MIGHT be true (even though we don't actually know)? There are three.

Anna has a huge library in her house. She ________ love books.

That woman drives a very expensive car. She ________ have a lot of money.

I can't find my sunglasses. They ____ be in my car. Or maybe I left them in the bar.

That woman drives a very expensive car. She ____ have a lot of money.

Paul is being very strange to me. I think he ______ be angry with me.

There's a bit of traffic, so I ______ not arrive in time.

You have walked for ten hours. You ______ be exhausted.

What modal verb do we use when we are SURE that something ISN'T true (even though we don't actually know)?

I think there ______ be a mistake in your tax return. You should check it