This is a question about half-life and probability. I asked the question on the Physics site and was told it is not a physics question by M. Enns. (https://physics.stackexchange.com/questions/368349/i-want-to-understand-the-probability-behind-half-life-maths-teacher).

I hope you can help me on this, I felt the half-life concept might better suit the physics community but I hope somebody can point me in the right direction.

If infinite men (called m1, m2, m3,…) all had access to one atom of the same radioactive substance (with a half life of Y units of time) each and each man follows the following pattern

M1 waits until 1 unit have time has passed. He checks if his atom has decayed and notes if it has or not. He then repeats this experiment for an infinite amount of time, with a new atom each time. M2 waits until 2 units have time has passed. He checks if his atom has decayed and notes if it has or not. He then repeats this experiment for an infinite amount of time, with a new atom each time. M3 waits until 3 units have time has passed. He checks if his atom has decayed and notes if it has or not. He then repeats this experiment for an infinite amount of time, with a new atom each time. And so on, and therefore

MY waits until Y units have time has passed. He checks if his atom has decayed and notes if it has or not. He then repeats this experiment for an infinite amount of time, with a new atom each time. If all men constantly calculated the probability of their atom being decayed after their amount of time had passed, one mans probability would eventually tend toward 0.5. Which man would this be?

If it helps my head is telling me it would be MY.

Thanks,

Ryan

• What's the point in repeating the experiment an infinite amount of times? Why not just calculate the probability that the atom decays after $n$ unites of time for any $n \in \mathbb{N}$? Nov 12, 2017 at 1:35
• I'm not sure. If I edit the question to that, could you give me an answer? Nov 12, 2017 at 1:36
• I'm just trying to understand your question. Of course I can answer my question, but I want to make sure it is the same as yours. I'm just wondering, why are you making these men repeat their experiments an infinite amount of times? It seems to me each man could just calculate (using probability, not experiment) the probability of decay in $n$ units time. Nov 12, 2017 at 1:39
• Oh I understand. Yes I think I am essentially asking as though they are calculating and experimental probability although we don’t need to set up such an experiment if we generalise it and consider mathematically. Nov 12, 2017 at 2:00

That is the definition of half-life. It is the duration which gives $\frac 12$ chance of decay. Yes, it would be MY.