The moon is about 1/4 the size of the earth so I suspect the chances of impact would be about 1/4 less than the chances of a bigun hitting us.
I don't think the size difference is what matters. I would guess that when you take into account the vast distances in the cosmos and the solar system, it is probably the same chance.
I might say that if you played a lottery with a billion to one odds, buying four tickets would not increase your winning potential four-fold.
that is true but the moon has a past history of getting lit up by asteroids as is evident on it’s dark side.