These types of probabilities are all over the place though. Even in chips with a billion transistors or more we have to design redundancy because manufacturing

These types of probabilities are all over the place though. Even in chips with a billion transistors or more we have to design redundancy because manufacturing at that scale isn't perfect. Imagine there's a 1 in 10 million chance of some sort of manufacturing defect on some modern processor; you're pretty much guaranteed 100 defects.