(I wasn’t able to find this specific question, so sorry if it’s been asked before)
Earlier today, I was told I would get a call between 5:00 and 6:00. If we make the assumption that this call is, for certain, going to occur within the specified time frame, I was under the assumption that every minute that passed would result in an increase in probability of the call would happen. For example, I was thinking that for the first minute the chance I get the call are 1/60, while the second minute would be 1/59 (as there are now only 59 minutes in which it could happen) and so on until the last minute is 1/1 (if I had still not received the call).
However, I was thinking back to my Freshman statistics course where my professor was talking about how the chances of the event happening at any given moment are the same, regardless of what time it is. In this case, at any given minute, the chance of me getting a call would still be 1/60. Unfortunately, I don’t remember any of the terminology that goes with these concepts, so I can’t remember if that actually applies to this problem.
So, in short, does the probability of something presumably inevitable increase as time passes? Or is the chance the same at any given moment?
In: Mathematics
In this case, since you have a window of time that the call *must* happen in, your initial thought is correct and at 5:59 if you haven’t gotten the call yet you know 100% it’s happening that minute.
If you only know that there is a 1/60 chance the professor will call you any given minute (no window where they must call you), then no matter how much time has passed it is still a 1/60 chance any given minute. Thinking it’s been so long there must be a greater chance now is the gambler’s fallacy (e.g. flipping a fair coin and getting heads 100 times in a row doesn’t mean that tails is due – there is still a 50/50 chance on the 101st flip).
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