June Trivia: The Monty Hall Problem

In this month's June trivia, we feature the famous Monty Hall problem

"Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, the others, goats. You pick a door, say #1, and the host, who knows what's behind the doors, opens another door, say #3, which has a goat. He says to you: 'Do you want to pick door #2?' Is it to your advantage to switch your choice of doors?"

This problem was used in many books and movies so some of you may have seen it before. It was featured in Mark Haddon's "The Curious Incident of the Dog in the Night-Time" (very good book) and the movie 21.

This question was posed to Marilyn vos Savant (person with the highest IQ in the world) in her September 1990 column "Ask Marilyn", and her answer was a source of major controversy.

Similar to the Monty Hall problem, the "Two Boys" problem also generated great debate in her column

"Say that a woman and a man (who are unrelated) each has two children. We know that at least one of the woman's children is a boy and that the man's oldest child is a boy. Can you explain why the chances that the woman has two boys do not equal the chances that the man has two boys?"