The Monty Hall problem (Challenge 1.5.18) was originally presented by Marilyn von Savant, writing in the "Ask Marilyn" column of Parade Magazine. She gave the correct answer. However, many people (including some well-known mathematicians, plus many laypeople) wrote in to complain that her answer was incorrect. The controversy dragged on for months, with many letters and very strong language written by both sides (in the end, von Savant was vindicated). Part of the confusion lay in the assumptions being made, e.g., some people misinterpreted her question as that of the modified version of part (e) of Challenge 1.5.18. However, a lot of the confusion was simply due to mathematical errors and misunderstandings. (Source: Parade Magazine, "Ask Marilyn" column, September 9, 1990; December 2, 1990; February 17, 1991; July 7, 1991.)
(a) Does it surprise you that so many people, including well-known mathematicians, made errors in solving this problem? Why or why not?
(b) Does it surprise you that so many people, including many laypeople, cared so strongly about the answer to this problem? Why or why not?