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Why is "Reports" in sentence down without "The":

Reports are coming in that a train has crashed near Birmingham.

This sentence is copied from the book How English Works by Michael Swam and Catherine Walter.

Why my question? Because I think that the plural "Reports" is a group of reports that have something together. It is new about "a train has crashed near Birmingham". For example, "The apples are red." Why not "Apples are red". I think because it is a group of red apples, not mix red, green, blue, etc.

Plurals do not require articles. If you use an article, you have a different meaning.

There are apples in the bowl. The apples are red.

The previously identified apples are red. Just like when used with a singular, the use of the definite article, the, indicates that you are talking about specific apples.

Apples are red.

This is a claim that apples, in general, are red. This is clearly an incorrect statement, as some apples have no noticeable red pigmentation at all. They are green (or, sometimes, more like yellow).

Apples are falling on my house.

Now, this isn't a general statement. It's not claiming that all apples in the world are falling your house right now. That would be alarming. It is saying that there are apples falling on your house. Similarly, we might say:

Reports are coming in that StackExchange is going to shut down.

This says that some reports are coming in saying that. If there was just one such report, we'd say "a report is coming in...". If we don't want to be precise about numbers, we just say reports.

I haven't sat down and explored this thoroughly, but it seems to me that a plural without article as the subject of a linking verb (be, look, seem, feel) is a statement in general about that category of item, possibly limited by context, and I suspect the same is true of verbs of state (stative verbs) and generally of verbs of perception (though I don't imagine inanimate objects being subjects of those very often). I'm not sure if there's a general rule for other action verbs, though. That's probably dependent on context. And of course negation changes things. For example,

Trains aren't running on the West Coast Mainline today.

That's a general statement. However,

Trains are running on the West Coast Mainline today.

That's not; not all trains are running on the West Coast Mainline, after all. However, this might be because the first could be rewritten:

No trains are running on the West Coast Mainline today.

Then there's an explicit determiner.

Essentially, you can consider most plural nouns as having a determiner - either explicit, or implicit. It's working out what the implicit determiner is that's the trick. In your example, it's clearly some. In others, it will be something else.

Not a native speaker. That being disclaimed, I would say that the reports in this context are general and not specifically known from previous situation. If it'd be only a single report, you'd say "a report is coming..." but since it's multiple instances of it, we can omit the.