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Life on Earth will be extinct before the sun expires because its future instability will make life on Earth impossible. Assuming that climate change and other events do not terminate life on Earth, so that there is an observer to watch the sun rise, there will be roughly a trillion (10^12) days before this happens, so the probability of the sun rising tomorrow is 100%. Probability assumes random chance, whereas the demise of the sun or Earth is based on scientifically predictable events which are not due to take place any time soon.

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