What is the probability of getting an academic job?

It is an interesting thought experiment that can be dissected in several ways depending on how it is addressed.

So, I figured why not just create github.com Shiny R application that builds estimates depending on the input. The current formula is a crude estimation that assumes there in an N population of positions that become available based on an independent probabiltiy p and there is a competing number of w applicants which are chosen at random. For CS and CE jobs in US and Canada based on CRA's survey data is around 50%.