Asteroid hits moon, debris hits Earth ?

It presumably has.

But if you do the math, you’ll find that statistically speaking it’s in the hundredths of a percent. IOW, negligible.

Even more significantly,

  1. Earth is geologically active, subducting old crust and generating new crust

  2. 70% of the surface is under water

That is a danger – thousands of times less likely then WWIII.