You could fly through it at random 1,000 times and never see a danged asteroid. One of the concerns of the catastrophe mongers is that a comet or other small body might pass near enough to an asteroid to perturb its orbit and drag it toward Earth. I wouldn't lose any sleep over the possibility. In the case of the room with the pinhead in it, an average comet is the size of a speck of dust. The chances of it perturbing the orbit of an asteroid in just the right way is very small indeed.
Space is vast, folks.
Comets, asteroids, and even planets inhabit a very tiny portion of the void. Still, a chance exists. Spread out over your lifetime, it's exceedingly small. Spread out over a million years, the odds are still smaller than the probability that humans will self destruct from war, poverty, disease, or ignorance. Our deepest fears and the need to titillate ourselves with them are the fodder of public funding.