SAYING WE ARE SURE SOMETHING WILL HAPPEN

We can use will and shall to talk about what will happen.

Exports will continue to rise over the next few months.
I shall be staying in Tokyo for the next three days.
We shan't stay long: we have to be at Mary’s by six.

• We can emphasise our certainty by adding really, (most) certainly / definitely, almost certainly, etc:
  You definitely won't like the exhibition.
  You'll certainly like their new CD.
  
  
•  We can express doubt by adding presumably, (most) probably, etc:
  You probably won't like their new single.
  You'll presumably be wanting some more.

Differences between shall and will

We use shall with I or we. It's old-fashioned with other persons:

I shan't have your X-ray results until next week.
You shall go to her party, I promise.

• When predicting something, or expressing determination, there is little difference in meaning between shall and will:
  We shan't / won't arrive much before midnight, I'm afraid. (= predicting)
  I shall / will succeed, just you wait and see. (= determination)

• But we use only will, not shall, to ask for predictions
  Will I get grade A, do you think?
  
•  We commonly use shall to make polite offers, or to ask advice:
  Shall I turn the lights on?
  Shall I wear the green or the blue tie?

SAYING IT IS POSSIBLE SOMETHING WILL HAPPEN

We use may, might and could to say that something is possible:

It may / might / could rain tomorrow.

• However, we commonly use will rather than may / might / could in questions:
  Will it ruin tomorrow, do you think?
  
•  We can also use would in conditional sentences to predict what would happen if something else happened, or to talk about things that are very unlikely to happen:
  He would get very annoyed if you rang him now.
  A sunny holiday in Wales? Now, that would be a miracle!
  
•  However, we can use will if other words in the sentence show that something is unlikely:
  I doubt if we'll ever again experience a winter quite as cold as this one.
  
•  We can emphasise the degree of probability by adding other words:
  She could conceivably come along a bit later. (= it's just possible)
  She may / might very well come along a bit later. (= it's quite likely)

• The situation, stress and intonation, and other words we use in the statement can affect the degree of probability more than the modal itself:
  I suppose she might come, but I doubt it. (= it's doubtful)
  Actually, I think she might very well come. (= high probability)

IN MY OPINION ...

We can use should and ought to to make subjective predictions. In the negative, we avoid oughtn't to, and prefer shouldn't:

They ought to / should win the next round easily.
You shouldn't have trouble with traffic.

• We use should and ought to to predict favorable events:
  She should fail her driving test.
  The weather should be horrible tomorrow.
  She'll probably fail her driving test.
  She should /ought to do well in her driving test.
  The weather will be horrible tomorrow.
  It should be fine tomorrow.