I was asked a question today which was What are the odds of the world ending on any date in the calendar in the future ? I have assumed it will end on one day I gave my answer as 364.25/1 on any day and 1460/1 on february 29th I was told that the odds are lower for december 4th at any time in the future than december 2nd in the future I cant see how this right Can anyone help please as i think i am right
Tell me more
×
Mathematics Stack Exchange is a question and answer site for
people studying math at any level and professionals in related fields. It's 100% free, no registration required.
|
|
Suppose that at midnight, Australian Eastern Daylight Time, the probability that the world will end during the next 24 hours is $p$ where $0\lt p\lt1$. So, the probability the world ends today is $p$. The probability the world ends tomorrow is $p(1-p)$; the world can only end tomorrow if it didn't already end today. In general, the probability the world ends on day $n$ is $p(1-p)^n$ (where today is day zero). For $0\le n\le364$, the probability the world ends on date $n$ is (ignoring leap years) $$Q_n=p(1-p)^n+p(1-p)^{n+365}+p(1-p)^{n+730}+\cdots=p\ {(1-p)^n\over 1-(1-p)^{365}}$$ Now it's clear that $$Q_0\gt Q_1\gt Q_2\gt\cdots\gt Q_{364}$$ |
|||
|
|
