The Monty Hall problem is a counter intuitive problem in probability mathematics that deals with picking the right prize from a set of three doors. The problem is named after the television celebrity Monty Hall and is loosely based on the USA game show Let's Make a Deal.
This has become a popular problem in programming as it is a good exercise in thinking through a problem to prove what outcome actually occurs. Lots of examples have been posted online so I thought I would sit down and attempt to solve it myself. The problem is most commonly summarised as follows (this example was taken from Rosetta Code):