# Help with simple stat formula

#### m160

##### New Member
Dear all,
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

#### Dason

Are the 2.5% randomly selected? And if somebody has been selected before does that impact their probability of being selected again.

#### m160

##### New Member
no, it is purely random and independent.
Is this ok ?
p(X=k)=(k,n) 0.975^k x 0.025^(n-k)
with n number of months and k number of time an element has been analysed over that period of time
so in my case k=0 and I am left with p(X=0)=0.025^n Is that right ? (not so rusty after all !)

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Would have to check on your equation but this seems equivalent to repeatsdly picking balls from an urn problem. So yca ball can be selected more than once over time for you?

Not sure if you are savvy enough but if you simulated this could create a graph of how many times each is probabilistically selected. May help audience relate.

#### Dason

That doesn't quite look right. I suggest when you come up with a solution try plugging values in and see if the solution makes sense. Always keep in mind what it is the values you're calculating are representing and see if it seems correct. Try plugging in n=1. Does the value you get seem reasonable?

#### m160

##### New Member
Actually it does: I did a simulation and a comparison with the results of a weighted decision tree. Why doesn't it "quite look right" ? Any rationale behind that ? What am I missing ?
Thinking about it, it is like repeatedly picking balls from a urn (e.g. 5 black balls and 195 white balls) and returning the ball to the urn before the new round.

#### Dason

So after one round there is a 2.5% chance of never having been analyzed?

#### m160

##### New Member
No 97.5%
After two rounds 95%, three 92.7%, etc.
What scares me is that it takes 27 rounds (i.e. more than two years) to see the chance of never having been analysed drop under 50% !
Picking 2.5% of the population is obviously not enough.