It's for all practical purposes impossible. Those dramatic movie and discovery channel videos use asteroids the size of planetesimals - hundreds or even thousands of kilometers in diameter.
There are asteroids that big. If Ceres or Vesta or one of the larger asteroids hit Earth it would indeed mean all life is wiped out probably. But they are in stable orbits for at least hundreds of millions of years. There is a 0.6% chance of Vesta hitting Ceres in any particular billion year period and even then - that's not a large asteroid hitting Earth, it's two large asteroids hitting each other.
The Earth, Moon, Mars, Mercury, were hit by really huge asteroids or comets over three billion years ago - but that was debris from the solar system as it was still settling down. The so called "late heavy bombardment" - the tail end of it.
But we haven't been hit by anything that big for over three billion years. The largest we can be hit by at the moment is more like 10 kilometers in diameter or a little larger. Jupiter may well have a lot to do with this, disrupting and diverting larger comets and asteroids from the outer solar system before they can be perturbed into Earth crossing orbits. Many end up hitting Jupiter, evaporating as they fly close to the Sun, or hit it, ejected from solar system, or if they survive all that, they get broken into pieces by tidal interactions with Jupiter.
So no, not going to happen. Indeed humans would survive and wouldnot be made extinct either - the flying dinosaurs (birds), mammals and many other creatures survived the Chicxulub impact. Humans with minimal technology would also.
And the chance is tiny. One chance in ten million, 99.99999% certain we won't be hit by even a 10 km diameter asteroid this century. Smaller asteroids are more likely and the tiniest the most likely of all. If we do get a news story "Asteroid due to hit Earth" it is almost certain to be a 10s to at most 100 meter asteroid as they are most common of all, so the most likely to be predicted. A 100 meter asteroid could be very devastating. But more likely to be smaller, perhaps 30 meters upwards.
And it is also almost certain to be predicted to hit a desert or remote area or the sea, because only a small percentage of the Earth surface is heavily populated.
So
HUGE ASTEROID DUE TO MAKE ALL HUMANS AND MANY OTHER SPECIES EXTINCT
- Not going to happen, just in movies
BIG ASTEROID DUE TO HIT EARTH, MOST OF THE POPULATION OF THE WORLD WILL BE MADE HOMELESS OR KILLED UNLESS THEY TAKE PRECAUTIONS - HOW TO PREPARE FOR IT
- that's extremely unlikely, 99.99999% certain it won't happen. But could do. It would lead to mass extinctions of many species. But humans are so adaptable is no way it would make us extinct - after all we can survive in the Arctic, or in the Kalahari desert, and almost anywhere in between.
SMALL ASTEROID TO HIT IN A REMOTE DESERT (OR IN THE SEA), BOOK YOUR FLIGHTS TO WATCH A SPECTACLAR FIREBALL AS BRIGHT AS THE MOON
- that's a far more likely scenario for the first predicted reasonable sized asteroid hit (we have already predicted a tiny meteorite, a few meters across, with a day or tow of warning).
If it is hazardous, then more like the Russian meteorite, watch out for broken windows and flying glass type scenario.
But you can't rule out a large asteroid impact which is why it is important that we detect them. And if necessary will eventually deflect them too. Because certainly this will happen. But it might be centuries or more likely thousands of years before we get hit by a largish one, even a 100 meter one is more likely not to happen for a few thousand years. After all there is no record of such an asteroid throughout human recorded history - no asteroid equivalent of Vesuvius. So they are rare. It's likely to be tens of millions of years before we are hit by a giant one like the one for the dinosaurs as they happen on average 100 million years ago (last one was 66 million years ago). It's just an average, can happen any time, but most likely to be many millions of years into the future. Plenty of time to deflect it to make sure it can't hit us. We can do that indeed with only a decade or so of warning, or even less for smaller asteroids, or using nuclear weapons to deflect or such like.
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