‘theoretical probability vs. experimental probability’ take a moment to reflect on that.
We are all drilled to some extend to accept probability theory, but there are some truly mind bending exercises in interpreting probability.
How do you define probability for a event that can only happen once, e.g. what is the probability of our cosmic microwave background pattern ?
How do you define conditional probability when conditioning on the assumption that an impossible event has occurred, e.g. what is the probability of the Color of my wall changing assuming Garfield the cartoon cat would enter the room?
> How do you define conditional probability when conditioning on the assumption that an impossible event has occurred, e.g. what is the probability of the Color of my wall changing assuming Garfield the cartoon cat would enter the room?
I mean mathematically you cannot apply a measure to something outside the space the measure has been defined on (the probability space is defined as the powerset of the set of possible values), so at least from a theory standpoint this question isn't that deep.
Actually it is, since measure theory and the Kolmogorov construction of probability is only one way to build an axiomatic theory of probability.
It just happens to be the one most of us learn first.
Its a bit like asking if the set of all sets that do not contain themselves is contained in itself. The question makes no sense in set theory, but it leads to important extensions.
We are all drilled to some extend to accept probability theory, but there are some truly mind bending exercises in interpreting probability.
How do you define probability for a event that can only happen once, e.g. what is the probability of our cosmic microwave background pattern ?
How do you define conditional probability when conditioning on the assumption that an impossible event has occurred, e.g. what is the probability of the Color of my wall changing assuming Garfield the cartoon cat would enter the room?