More fine prints … this time the Law of AND
In order for the Law of AND to work, the two events have to be independent. What does that mean? It means that one event does not influence the other. The fact that one event has occurred does not make the other more likely.
For example, getting hurt and going to the hospital are NOT independent events. My chances of getting hit on the head by a falling tree this year are maybe 1 in a hundred, or 1%. My chances of going to the emergency room this year are maybe also 1%. So using the Law of AND, my chances of getting hit in the head and going to the hospital would be 1% × 1% = 0.01 × 0.01 = 0.0001 = 0.01%, or one-hundredth of a percent.
But in fact, IF I get hit in the head, I’m likely to want to go to the hospital for that very reason. So, the two events are NOT independent!! And my chances of getting hit in the head and going to the hospital are much bigger than 0.01%. Maybe more like 0.5% (about half the time that I get hit in the head I go to the hospital).
My street after the last tropical storm —
luckily I did not get hit by this falling tree!