Statistically speaking, Finding a second unique object

[syano]

*This is probably not the best area for this thread. Sorry about that. I couldn’t find another area that seemed much better than this one. Please feel free to move it to whereever… Thanks,*

This question has been bugging me for a long time and I am hoping I can get some insight on the topic.

Please allow me to not directly ask the question because I am looking for non bias or zealous answers.

Say you find a unique object in your yard. Let’s call this unique object a Widget. Now let’s say you want to see if you can find another one so you search your entire yard, which is 1000 square feet, for another Widget. Let’s say you do not find another Widget in your yard.

What are the odds you will find a second Widget if you search your neighbors yard which is 1000 square feet also?

Let’s say you do not find another Widget in your neighbor’s yard… So far you have found one Widget in a total of 2000 square feet.

What are the chances you will find another Widget if you search an addition 1000 square feet as compared to an additional 2000 square feet?

If you still do not find a second Widget… Will your chances continually increase of finding a second Widget the more area you search or do they remain the same until you find a second Widget?

If we find 2 Widgets in 5000 square feet it makes sense to me to say we would be likely to find 2 more Widgets if we search another 5000 square feet. But if we only find 1 Widget in 5000 square feet could we still say we would be likely to find a second Widget if we search another 5000 square feet?

 

[russ_watters]

This sounds a lot like the issue with the Drake equation.

Probability is relatively straightforward mathematically: 1 widget in your yard of 1000sq ft is 1/1000 widgets per square foot. Based on that, if you search your neighbor's yard, the chances are 1/1000 that you'll find a widget on any individual square foot of space. But if you don't, now you have more info on the odds: now its 1/2000 for the next yard and so on.

However, you could also say that you have 1 widget per yard. Based on that, you may calculate the probability of finding a widget in the next yard to be 100%. But that really isn't all that meaningful, is it?

The issue here is clear: with such low instances of widgets found, it is extremely difficult to get a meaningful probability for a future search. The more searches you do, however, the more info you have on what the probability really is.

With the Drake equation, some people will start with a 1/1 probability that an earthlike planet (whatever that means) will have intelligent life. Seems reasonable, right? - we only know of one earthlike planet and it has intelligent life on it. But that's a mis-application of probability.