(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
FWIW, drawing cards (or some other random variable) without replacement is only one possible situation that can underlie “getting a call between 5 and 6.” That scenario evenly distributes the probability of a call across the entire hour, but that probability may be unevenly distributed.
For example, maybe the person who is trying to call you has a meeting scheduled at 5. If that meeting is cancelled, they will call you at 5 precisely. If not, they likely won’t call you until after 5:30. This could make the probability of getting a call at 5:15 lower than the probability of getting a call at 5, *even conditional on reaching 5:15*. To think about it in terms of drawing cards from a deck, imagine sometimes getting to draw more than one card and sometimes getting to draw no cards at all.
Without knowing more details about the schedule of the person who will call you, it’s fair to approximate the probability of a call with an equal chance each minute, but that’s not necessarily what’s actually going on.
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