Attempt to solve #115 “A random robot” puzzle from the New Scientist. This week (No 3336 - 29 May 2021) the New Scientist published the following puzzle:
Roman the test robot is being given one final roam before being consigned to the scrapheap where he can rust in peace.

It is usually taught in statistics classes that Binomial probabilities can be approximated by Poisson probabilities, which are generally easier to calculate. This approximation is valid “when \(n\) is large and \(np\) is small,” and rules of thumb are sometimes given.

I present a solution to a modification of the “hardest logic puzzle ever” using probability theory.
Background “The hardest logic puzzle” was originally presented by Boolos (1996) and since then it has been amended several times in order to make it harder (see Rabern and Rabern 2008; Novozhilov 2012).