Probability space consists of three things: sample space, event space and probability function.
Sample space defines a set of possible outcomes of probability experiment, representing the knowledge state of the person participating in it. In this case its:
{Odd, Even}
For event space we can just take a superset of the sample space. And as our measure function we just need to assign probabilities to the elementary events:
P(Odd) = P(Even) = 1⁄2
Do I understand correctly that the apparent problem is in defining the probability experiment in such a way so that we could talk about Odd and Even as outcomes of it?
We don’t??? Probability space literally defines set of considered worlds.
Probability space consists of three things: sample space, event space and probability function.
Sample space defines a set of possible outcomes of probability experiment, representing the knowledge state of the person participating in it. In this case its:
{Odd, Even}
For event space we can just take a superset of the sample space. And as our measure function we just need to assign probabilities to the elementary events:
P(Odd) = P(Even) = 1⁄2
Do I understand correctly that the apparent problem is in defining the probability experiment in such a way so that we could talk about Odd and Even as outcomes of it?
The problem is “how to define P(P=NP|trillionth digit of pi is odd)”.
Interesting. Is there an obvious way to do that for toy examples like P(1 = 2 | 7 = 11), or something like that