I am doing a presentation on a medico-legal issue and I would like to show the probability of an event over time. It has been ages since I last used statistics and I am a bit rusty, to say the least...

2.5% of a large population (50K) is analysed every month. What is the probability over time of "never have been analysed" ?

I though of a binomial or a poisson function but when I had a look at the formulas and explanations (wikipedia) I was deeply confused... Any idea how I can adapt this formulas ?

Many thanks !

M