Probability question/s

[#1procrastinator]

Why do we multiply two sets/probabilities to find their intersection?

[TrueTears]

Simple answer: It just comes intuitively from the multiplication rule and the classical definition of probability (#number of success/#number of total observations) , http://en.wikipedia.org/wiki/Classical_definition_of_probability

Complex answer: In fact we can formalise and make probability extremely rigorous, under certain conditions there is no need to think intuitively and all operations are mapped out formally. This is the idea behind a probability space generated by sigma algebras:

http://en.wikipedia.org/wiki/Probability_space#Definition

http://en.wikipedia.org/wiki/Sigma-algebra#Definition_and_properties

Especially note that:

From these axioms, it follows that the σ-algebra is also closed under countable intersections (by applying De Morgan's laws).

Although the definition of a sigma algebra does not contain intersections, it is a direct implication from it.

Needless to say, in highschool and elementary probability, I think the intuitive way suffices.

[#1procrastinator]

lol crazy thanks TT