MHProb - A Program to Illustrate the Monty Hall Problem

There was a television gameshow in the US in the 1970's called "Lets's Make A Deal", the host of the show was Monty Hall. The show was fairly simple. A contestant is faced with three closed doors there is a car behind a random one of the doors and a goat behind the other two. The contestant, who is unaware of what lies behind each of the doors, is asked to select one of the doors and to inform Monty of his selection. Monty will then open one of the unselected doors that has a goat behind it. The contestant is then asked if he will stick with the original door he selected or switch to the other unopened door. Having changed (or not) his selected door, the remaining doors are flung open to see if the contestant has won the car (I believe that if his door had a goat behind it then he did not win the goat!). The "problem" arose, not because of the gameshow itself but from a letter from Steve Selvin to the American Statistician in 1975 and then further discussed in Marilyn Vos Savant's "Ask Marilyn" column in Parade Magazine in 1990. The column discussed if the contestant would have a winning advantage if he stuck with his original door or switched to the other unopened door. Savant argued that the contestant should switch as that had a 2/3 probability of winning the car rather than a 1/3 probability of winning if he stuck with his original selection. Here lies the problem, an overwhelming 87% of people were in favour of sticking with the original selection leaving only 13% trusting in Savant's analysis. See https://en.wikipedia.org/wiki/Monty_Hall_problem for a detailed discussion. The MHProb program illustrates the problem and provides a series of scenarios that demonstrate the corectness of supporting the "switch" strategy.