Yes, this is correct. For example, give most people most vaccines, and they will be fine. However, some vaccines will cause a few people in every 100,000 or so

Yes, this is correct. For example, give most people most vaccines, and they will be fine. However, some vaccines will cause a few people in every 100,000 or so to develop ITP, which can mean a brief period of bruising and bleeding (as your immune system eats your blood platelets) that clears up with simple steroids, or it can mean longer term or even chronic illness, splenectomy, even death. We have zero way to predict this for any given person. The same is true of other "rare" reactions.