Was the pager message from Nick Fury to Captain Marvel unnecessary?

"She'll find out eventually" isn't good enough. Earth is in trouble right now. Captain Marvel needs to find out right now. It's unclear how much time has passed between the snap and her arrival back on Earth in Captain Marvel's post-credits scene, but she didn't get there immediately, so the sooner she found out, the sooner she would arrive.

As for the 50% chance, I don't think Fury knew exactly what was happening. He doesn't appear in Infinity War until the post-credits scene, and IIRC, there's no indication he knew about Thanos or his plan to wipe out half the universe. All he knew was that, across the planet, people had started disintegrating. He had no way of knowing that Captain Marvel herself could potentially have been affected.

Wherever she is, Carol knows half of everyone disappeared. Everywhere's in trouble.

What Carol doesn't know was that Fury has a team who is fully involved and caught up on the actual root problem, and can brief her in minutes. And they are her best hope to put her capabilities to work quickly and effectively on the problem. In a coordinated way, with the support of others.

That, then, is the purpose of the page.

There is no way to know if she would have come to Earth. Carol might not have been aware of Thanos, or the Earth was at the core of events. She could easily have guessed it was limited to the Skrulls, Kree, or wherever she happened to be at the time. Even after she learned it was more widespread, there is no reason for her to go straight to Earth.

Similarly, no-one (at least shown on screen) told Fury what was happening. He knew aliens attacked Earth, and that people started Dusting. It is no major leap to guess the events are connected. But it is a much bigger leap to guess it is universal. Either way, Fury's focus has always been Earth, so he wants to call one of his strongest assets back. Especially since he knows the Avengers are splintered after Civil War.