If this was true, then we could not observe the event „any other coin sequence“ as well since this event is by definition not being tracked.
When you are tracking event A you are automatically tracking its complement.
In fact, in order to detect a correspondence between a coin sequence that we have in mind and the actual sequence, our brain has to compare them to decide if there is a match. I can hardly imagine how this comparison could work without observing the specific actual sequence in the first place. That we classify and perceive a specific sequence as „any other sequence“ can be the result of the comparison, but is not its starting point.
Oh sure, you are of course completely correct here. But this doesn’t contradict what I’m saying.
The thing is, we observe a particular outcome and then we see which event(s) it corresponds to. Let’s take an example: a series of 3 coin tosses.
So, in the beginning you have sample space which consist of all the elementary outcomes:
{HHH,TTT,HHT,TTH,HTH,THT,THH,HTT}
And an event space, some sigma-algebra of the sample space, which depends on your precommitments. Normally, it would look something like this:
Because you are intuitively paying attention to whether there all Heads/Tails in a row. So your event space groups individual outcomes in this particular way, separating the event you are tracking and it’s complement.
When a particular combination, say THH is realized in a iteration of the experiment, your mind works like this:
Outcome THH is realized
Therefore every event from the event space which includes THH is realized.
Events {HHT,TTH,HTH,THT,THH,HTT} and {HHH,TTT,HHT,TTH,HTH,THT,THH,HTT} are realized.
P(HHTorTTHorHTHorTHTorTHHorHTT)=2/3
This isn’t a rare event and so you are not particularly surprised
So, as you see, you do indeed observe an actual sequence, it’s just that observing this sequence isn’t necessary an event in itself.
When you are tracking event A you are automatically tracking its complement.
Oh sure, you are of course completely correct here. But this doesn’t contradict what I’m saying.
The thing is, we observe a particular outcome and then we see which event(s) it corresponds to. Let’s take an example: a series of 3 coin tosses.
So, in the beginning you have sample space which consist of all the elementary outcomes:
{HHH,TTT,HHT,TTH,HTH,THT,THH,HTT}
And an event space, some sigma-algebra of the sample space, which depends on your precommitments. Normally, it would look something like this:
{∅,{HHH,TTT},{HHT,TTH,HTH,THT,THH,HTT},{HHH,TTT,HHT,TTH,HTH,THT,THH,HTT}}
Because you are intuitively paying attention to whether there all Heads/Tails in a row. So your event space groups individual outcomes in this particular way, separating the event you are tracking and it’s complement.
When a particular combination, say THH is realized in a iteration of the experiment, your mind works like this:
Outcome THH is realized
Therefore every event from the event space which includes THH is realized.
Events {HHT,TTH,HTH,THT,THH,HTT} and {HHH,TTT,HHT,TTH,HTH,THT,THH,HTT} are realized.
P(HHT or TTH or HTH or THT or THH or HTT)=2/3
This isn’t a rare event and so you are not particularly surprised
So, as you see, you do indeed observe an actual sequence, it’s just that observing this sequence isn’t necessary an event in itself.