Ian Stewart explains the Monty Hall problem and its solution.
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The Monty Hall problem became infamous in the 1990s where newspaper columnist and puzzle solver Marilyn vos Savant offered a solution to it that, despite being right, was so counter intuitive that hundreds and thousands of people refused to believe her.
The problem takes the shape of a game show, where there are three doors. Behind two of the doors there are booby prizes - goats, and behind one door is the big prize - a sports car.
The contestant is asked to pick a door. The host, who knows what's behind each door opens one of the other two to reveal a goat. At this point the contestant is offered the choice of either sticking with their initial pick or swapping to the other remaining door. Should the contestant make the swap?
Ian Stewart gave the 1997 Christmas Lectures "The Magical Maze" about hows how maths governs almost every aspect of our lives, ranging from our birthdays to American game shows, calling in at panthers, petals, and the logic of chaos.
The third lecture in the series is all about probability.
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