So what are the chances that a 98 Lumina with the 3.1L V6 with 180,000miles has a blown head gasket?
My mom took her car to her mechanic, because the antifreeze was black, and she had not heat. He says its a blown head gasket $1000 to fix it. Sounds a little fishy to me, so i call another mechanic, and he said most likely its a Intake gasket, which to me sounds more like it. So my mom called her mechanic again, and asked if it could be the intake gasket and he said nope its the head gasket.
So whats the possibility that it is actually a head gasket.

Very high probability. The 3x00 60* V6 is known for blowing head gasket(*). Did they do a compression check to determine a bad head gasket? Most likely the head gasket went.

compression check FTW!

Compression test might show it if the leak is bad enough. Blown head gasket usually leaks the other way...coolant gets sucked into the cylinder on the intake stroke, with a little pressure going back into the coolant on the compression and power strokes. You get a little coolant in the oil, but the bulk of it flashes into steam and goes out the exhaust.

I'm curious what the "black" in the coolant looks like. Is it degraded rubber from the hoses, carbon, oil, or cooked ATF ?

In truth, the 60 degree V6 does have a history of blowing head gaskets, but I would not jump to that conclusion just yet.