B About the naive definition of probability

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The naive definition of probability requires equally likely outcomes and is limited to finite sample spaces. A biased coin cannot be accurately modeled using this definition, as it does not produce equally likely results for heads and tails. While one could create multiple events for heads to fit the model, these do not represent observable differences. Despite being labeled "naive," this definition is fundamental for understanding basic probability problems. However, it is insufficient for addressing more complex scenarios in probability theory.
red65
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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?
 
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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.
 
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ok, thanks a lot!
 
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