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But you're Muggle-born, so someone from the school will have to come and explain to your parents.

Okay so Harry isn't Muggle-born, but he is Muggle-raised as the Hogwarts admission committee probably knows.

Just before Harry's first year, why did Hogwarts send so many letters instead of just having Hagrid or someone go in the first place?

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If Hagrid's reaction upon finding out that Harry doesn't know anything about Hogwarts or magic is any indication, everyone at Hogwarts fully expected Harry to already know about the magical world (emphasis Rowling's):

[Y]eh'll know all about Hogwarts, o' course.

"Er - no," said Harry.

Hagrid looked shocked.

"Sorry," Harry said quickly.

"Sorry?" barked Hagrid, turning to stare at the Dursleys, who shrank back into the shadows. "It's them as should be sorry! I knew yeh weren't gettin' yer letters but I never thought yeh wouldn't even know abou' Hogwarts, fer cryin' out loud! Did yeh never wonder where yer parents learned it all?"

"All what?" asked Harry.

"ALL WHAT?" Hagrid thundered. "Now wait jus' one second!"

He had leapt to his feet. In his anger he seemed to fill the whole hut. The Dursleys were cowering against the wall.

"Do you mean ter tell me," he growled at the Dursleys, "that this boy - this boy! - knows nothin' abou' - about ANYTHING?"

Philosopher's Stone Chapter 4: "The Keeper of the Keys"

This doesn't seem an unreasonable assumption, since Petunia's sister was a witch and since the Dursleys were given a letter by Dumbledore "explaining everything":

"His aunt and uncle will be able to explain everything to him when he’s older. I’ve written them a letter."

Philosopher's Stone Chapter 1: "The Boy Who Lived"

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