What Is the Probability that the Sun Will Rise Tomorrow? — Sunrise Problem

Photo by JOHN TOWNER on Unsplash


You have lived n number of days and all the days you lived, you have seen sun rising. What is the probability that the sun rises tomorrow?


Let the risings be independent identical indicator random variables and S[n] be the sum of them. Given that we have seen n risings, the fact we know is:
S[n] = n


The earliest memory (at least) I can remember of is tearing apart of photo album cover at the age of 9. Today, I am 23. During this time, I have lived at least 5000 days and never ever has the sun not risen.


I also wanted to see how PDFs vary with n. Intuitively speaking, with the increase in value of n, the density should be more and more concentrated around higher probability values (say 0.8–1.0).

Fig (I) PDFs of p for different values of n


When I know nothing about you, I am 50/50 on you. I do not really have an opinion about you. You might be friendly, you might be unfriendly. I might like you, I might not. You might like me, you might not. Everything is 50/50. To see this, let’s plug n=0 in our formula, it results (0+1)/(0+2) = 1/2.

First Impression is the Last Impression

First meet is considered with high importance. First business deal is treasured. First goal in the football game is celebrated. First wicket in cricket created nervousness in the dressing room. First things tend to get importance. Why so?



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Suraj Regmi

Suraj Regmi


CS Graduate Student at UAH, Former Data Scientist at World Bank — the views and the content here represent my own and not of my employers.