Chance of finding a tree in a sample area If I have 83 trees appearing over 24 quadrats (a quadrat being a 10m x 10m sample area => 2400m^2 total area), what's the chance of finding a tree in a sample area? What's the chance of finding a tree per m^2?

Given no more information, the chance of a particular tree being in a given quadrat is $\frac 1{24}$. Therefore the chance of the tree not being in the quadrat is $\frac {23}{24}$. Lacking any other information, we assume that the placement of the trees is independent (a dubious assumption, since trees tend to cluster because of how they propagate). Therefore the chance of our quadrat not having any of the 83 trees would be $\left(\frac {23}{24}\right)^{83}$.

And thus the probability that our quadrat does have a tree in it is $$1 -\left(\frac {23}{24}\right)^{83}$$

The calculation for sample sizes of $1\; m^2$ is similar.