Probability of past vs future events

[bahamagreen]

Does probability apply to past events before determining the outcome?
Does the probability of an undermined past outcome change to p=1 when the outcome is revealed to have occurred?
Does the probability of a future event change to p=1 after it happens?

I may have more questions, probably depending on the answers... ;)

 

[Naty1]

Does probability apply to past events before determining the outcome?

you can determine the probability of a past event having happened; but the specific outcome is now certain.

Does the probability of an undermined past outcome change to p=1 when the outcome is revealed to have occurred?

you mean 'undetermined'?


Does the probability of a future event change to p=1 after it happens?

Same as #1.

I may have more questions, probably depending on the answers... ;)



I am not certain what you are building to here, but if you consider some events, like rolling of dice, the past probability and the future are the same...but if you are drawing from a deck of cards,for example, past outcomes do affect future probabilities.

 

[Naty1]

If you want sophisticated analyses, posting in the mathematics section might draw the widest experts...

 

[bahamagreen]

Let's take a single particular case of flipping a coin and look at what we would assign as the probability for heads before the flip, after the flip but before looking, and after looking.

At 1pm a plan is conceived to flip a coin at 2pm, and observe the results at 3pm.

We would state the probability of heads for this particular flip at 1pm is p=.5
The coin is flipped unobserved at 2pm...
At 3pm we observe a heads...

Is p=.5 still in force between 2pm and 3pm?
What about after 3pm (for this single case, specific, individual, historical, actual, completed flip)?

After 2pm the event and result have already occurred yielding a particular outcome, though unknown. The status of the unknown outcome is existentially identical to any outcome in the past - it is fixed. We may not yet know what state it is, but continuing to treat p=.5 for this event past 2pm seems incorrect... its actual state is either 1 or 0, not .5
I understand that some will say the chance of heads being observed is still p=.5 until the observation at 3pm, but it seems that after the fact of the coin flip there is no chance involved, just not knowing until observation.
The distinction I'm seeing is between predicting what the observation will be, and noticing that the state of the coin is already settled and just awaiting observational confirmation. Chance was finished after the flip and does not seem to have any role between 2pm and 3pm. The chance of guessing right is p=.5, but the actual condition of the coin is done...
Not knowing if it is 1 or 0 does not seem to justify calling it .5 since that is not either of the answers for either of its two current possible existing states - one of which it is definitely in.

After 3pm, is the "historical" probability of this particular flip now p=1? Meaning, since we know the heads result is now a known fact that actually happened, that particular individual flip can't be p=.5 anymore, it has to be 1.

Think of it this way... the classic experiment is to flip a coin 100 times and tally heads and tails. Call heads 1 and tails 0...
Before you flip the first coin, heads is p=.5
The flip shows heads, so you write down "1"

What you don't write down is ".5" because you have a historical individual result of "1"... is that not the same as recording the probability of that individual historical flip as p=1?