A black hole has been spotted heading towards Earth, and we have 200 years before it arrives. Does our species have a chance of survival?
Perhaps. But not on Earth. (Assuming any kind of astronomically plausible black hole, there is no way of avoiding substantial perturbation of the Earth’s orbit followed by tidal distortion and probable destruction of the Sun.)
However, it may be possible to colonize some asteroids and by small manipulation of their orbits ensure that they get slingshotted so as to end up at sufficient distance from the accretion disc (into which the sun and planets will be converted by tidal forces) so that the body of the asteroid is sufficient to shield its residents from the radiation.
Since the colonies will of necessity be small, most humans will be stuck on Earth and not survive; but if sufficient genetic diversity is brought along in the form of germ cells and/or frozen zygotes or blastocysts then perhaps the species itself might survive and adapt to the new low gravity environment.