Branching a discussion from Is a coin more likely to flip tails if it has already flipped heads a bunch?:
I don’t know how to answer this question. I lean towards ‘no’, but I think it’s a complex question (and as a result not very useful for clarifying the basics of probability, thus the new thread)
The reason I lean towards no is that, though the sun is expected to burn out eventually, it’s not expected to do so suddenly. I’m unaware of any theory that suggests that could happen, or any observation of a star like our sun suddenly extinguishing. So while I think there’s good reason to believe it will one day be extinguished, it doesn’t seem like the likelihood of it extinguishing increases every day. Kind of like how even though we know it will eventually be Christmas, it’s not getting increasingly likely that tomorrow is Christmas.
I could be wrong on a number of points of solar physics, and if solar extinction works differently my answer may be different.
More likely than the sun not rising because it went out is that sun won’t rise because we’re wrong about the nature of reality, e.g. we are mad, or we live in a simulation, or we’ve been lied to by a vast conspiracy of astrophysicists. To be clear, I don’t think any of these is particularly likely (though madness is the obvious favorite), I just think it’s very, very, very unlikely that the sun will go out tomorrow if modern science’s best guess of how stars and planets work approximates how stars and planets actually work.
And I’m not sure how the likelihood of those changes over time. The odds of a conspiracy seem to decrease as our lives increase, since it’s harder to fool someone for longer. The odds of madness seems to decrease for a similar reason, though if we’re mad I’m not sure we can trust reasoning at all. The odds of it being a simulation seem to increase, because new technologies continue to expand what might be possible with technology – when the greatest computer on earth was the Antikythera mechanism, it would have been hard to convince anyone that we could be constructs inside a computer, and rightfully so.
I don’t know how to net that out, because it’s very hard to put numbers to such improbable and bizarre hypotheses (particularly when they threaten to undermine the very bases of our reasoning about them). It seems possible that the total of these outside possibilities is either increasing or decreasing, and in any case it is a rounding error against the already vanishingly small possibility that the sun won’t rise tomorrow.
So I think it’s hard to give a firm answer, I lean ‘no’ but I have a lot of uncertainty about it. I think it’s very hard to put an exact estimate on the probability of the sun rising tomorrow that is better justified than ~1.