82% of an event in a persons life, what is the daily chance? If there is an 82% chance that within your average lifetime, lets assume 70 years (25567 days), that "E" event will happen: what is the percent chance that it will happen on any given day?
I'm assuming that it'll be something like .02347% or something small. My problem is I've only taken up through Advanced Algebra and that was six years ago. I would have searched for this on google to solve it myself, but I'm not even sure what to call this beyond "math I don't know". 
So if you could help me identify the solution, how to solve it, and what this is (i.e. I imagine terms like 'graphing polonomials' 'deductive statistics' or some such name that would give me an idea of what exactly it is that I should be learning to handle similar questions on my own). Thanks for the help in advance.
 A: If the probability that it happens in a specific day is $p$, then the probability that it does not happen is $(1-p)$ (complimentary events). Thus the probability that it will not happen in $25567$ days is $(1-p)^{25567}$ (product rule, independent events). Therefore the probability that it will happen in a lifetime is $1 - (1 - p)^{25567}$ (again, complimentary events), and that is your $82\%$.
So, we have that 
\begin{align}
0.82 &= 1 - (1-p)^{25567} \\
0.18 &= (1-p)^{25567}\\
\sqrt[25567]{0.18} &= 1 - p\\
0.999933 &= 1-p\\
0.000067 &= p
\end{align}
so the probability of it happening in a given day (assuming it doesn't change with day of the week, time of the year, age, and so on) is $0.0067\%$.
This is a bit backwards from the standard textbook example (it would give you the daily probability and ask you to calculate the lifespan probability), but it's more or less elementary probability, as they should teach in any high school. The two main concepts used in setting up the first equation was complimentary probability and the product rule. Once the equation was set up, however, we basically forget all about the probability, and focus on the algebra of isolating and calculating $p$. When we have that, we go back to the probability interpretation, and say what it means.
A: A statistic that said if you live to be 70, your chance of being the victim of violent crime is 82% would be better expressed as "your chance of being the victim of one or more violent crimes" and couldn't really be used to calculate the daily probability.
