In my previous post, I presented the famous Monty Hall Dilemma that sparked a maelstrom of controversy in 1990 and beyond. In that post, I presented three of the emotional responses from Ph.D.’s who declared Marilyn’s answer was wrong. There were many more vitriolic responses from mathematicians (see Intelligence, IQ & Perception pp. 220-224) However, there was an interesting follow-up from other Ph.D.’s and even from elementary schools.
You may recall that Marilyn’s initial response was:
Dear Craig:
Yes, you should switch. The first door has a 1/3 chance of winning, but the second door has a 2/3 chance. Here’s a good way to visualize what happened: Suppose there are a million doors, and you pick door number 1. Then the host, who knows what’s behind the doors and will always avoid the one with the prize, opens them all except door number 777,777. You’d switch to that door pretty fast, wouldn’t you?
However, those who wrote angry letters, did not address her reasoning, but mainly reiterated their original assumption that the probability for each door remains at 1/3. Others merely assumed that all these Ph.D.’s couldn’t be wrong, and merely piled on. To the letter from E. H., (see previous post) Marilyn could have answered, “Yes, indeed, the country is in trouble when so many Ph.D.’s in mathematics fail to challenge their assumptions and move too quickly to certainty.”
Some respondents were so sure that Marilyn’s answer was incorrect, that they were prepared to wager bets as high as $20,000 that she was wrong. To her credit, Marilyn showed grace under fire and kept cool. To a letter from Don. E. in Sunriver, Oregon stating, “I think you’re still wrong. There is such a thing as female logic,” she responded, “Oh hush, now.”
On the positive side, there were many mathematicians who came to the defence of Marilyn’s answer. The letter shown below from Steven Turner is just one example.
Dear Ms. Savant,
… Your solution is the correct one and any REAL mathematician can produce a proof of its correctness. REAL mathematicians consider this a trivial problem. WHAT discipline do these respondents have their PH.D.’s in? Is it adolescent behavior? If it is in mathematics, my second question is what institution granted it? Really, their behavior is so disgusting I have lost sleep over it. …
Good luck and good wishes from Massachusetts.
Sincerely, Steven J. Turner, Professor of Mathematics, Babson College
The letters reveal that, even some professional mathematicians, whose job involves scrutinizing logical arguments, are guilty of confirmation bias–our tendency to seek confirmation rather than disconfirmation of our beliefs.
In the years that followed, math teachers in elementary and secondary schools engaged their students in the investigation of the Monty Hall Dilemma through experiment–called Monte Carlo methods. The two letters shown here are a credit to the teachers who motivate their students using “real-world” applications of mathematics.
Dear Marilyn:
Our class, with unbridled enthusiasm, is proud to announce that our data support your position. Thank you so much for your faith in America’s educators to solve this . – Jackie Charles, Henry Grady Elementary, Tampa, Florida
Dear Marilyn:
…Your problem was presented to 240 students, who were introduced to it by their science teachers. They then established the experimental design while the mathematics teachers covered the area of probability. Most students and teachers initially disagreed with you, but during practice of the procedure, all began to see that the group that switched won more often. We intend to make this activity a permanent fixture in our curriculum – Anthony Tamalonis, Arthur S. Sommers, Intermediate School 252, Brooklyn, New York
In her book, The Power of Logical Thinking, Marilyn reported:
Of the letters from the general public, 92% are against my answer; and of the letters from the universities, 63% are against my answer. Overall, nine out of ten readers completely disagree with my reply.
So, having a Ph.D. in a particular field does not save you from making mistakes; it merely makes you correct more often than the layman.
