About the naive definition of probability

[red65]

hello, I took an introductory course about statistics, we viewed the naive definition of probability which says "it requires equally likely outcomes and can't handle an infinite sample space ", I understood that it requires finite sample space but I didn't understand "equally likely outcomes ", does it mean that if we have a coin with no equally likely heads and tales that do not satisfy the naive definition?

 

[Office_Shredder]

That's right, a biased coin cannot be modeled as two events, one heads and one tails, because in the naive model all events are equally likely.

You can kind of jam it in if you squint, e.g. ifthe coin is 2/3 to be heads, then have events H1 and H2 which are both the coin landing heads, and T which is the coin landing tails. But H1 vs H2 is not an observable difference.

 

[red65]

ok, thanks a lot!

 

[FactChecker]

You can call it "naive" but it is an important, basic subset of the problems. And many problems are a series of steps where each step is of that type. But it will not get you very far; there are too many problems that are not like that.