How do the Voyger probes avoid things like the astoroid belt when traveling at 20 - 30,000 miles an hour?

because as their name suggests they are in a belt - so there are large areas where there are very few asteroids and then only very small ones (grains of sand size) so the probe is sent on a track to avoid the main part of the belt.

a) The volume of the asteroid belt is massive, so is the volume between asterods and it is thus very inlikely that Voyager or any other space probe will occupy the same space-time as an asteroid

b) (this is less well known) The actual speed does not matter! A probe going faster sweeps out a greater volume BUT spends less time in each part of that volume. (Of course if it DOES hit then the damage is greater)

The asteroid belt is not very dense. You would actually have try to hit an object there to

hit one. Interplanetary dust and small particles are an issue, and no doubt these probes do

get hit by small stuff.

Because in reality - the space between the asteroids is HUGE - it is not a case of point and hope - there are literally hundreds of thousands of miles oe free space to get through

They don't!! You have to remember that although there are a lot of asteroids, the average distance between them is very large. This reduces the chance that something the size of Voyager will hit one of them.