ah conditional probability. I wonder how many thousands of years of development we as a society have lost from a lack of understanding of this concept.

If there is a piece of maths that should be drilled into every student more than any other, its at least a vague understanding of the difference between joint and conditional probability. and the underlying knowledge the ability to make this distinction implies. Much more likely to be useful to a randomly selected daily life than trig, calculus or geometry.