Yet Another Math One

SamuelRSmith

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SamuelRSmith on 02 June 2007

Roght I get it. You're not guaranteed to win, but switching gives you the higher chance.

jlauro

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jlauro on 02 June 2007

DRJ said:
Yeah you switch cause the announcer has a limited choice, he can only pick one that doesnt have the item. Since his choice is constrained you get better odds. An easy way to look at it is if there were 100 boxes and you picked 1, then the announcer says I will open 98 that don't have the item, then do you want to switch. The choice would be very obvious.

Actualkly that does make it easier to understand. However, if given the chance to switch after each box, you don't want to switch until the last possible moment...

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Lingyis on 02 June 2007

Okay, it indeed seems improbable that Math professors and Ph.D.'s get it wrong! Again, hindsight is 20/20. Many important discoveries and theories seem trivial--they make you think: "People took that long to figure that out?"

Here's more details about how people were getting it wrong. From "The Power of Logical Thinking" by Marilyn Vos Savant, who according to some has the highest I.Q. on the planet. Starting on P.6, there are about 20 quotes on PhD's getting it wrong. Examples:

"... As a professional mathematician, I'm very converned with the general public's lack of mathematical skills. Please help by confessing your error and in the future being more careful." (R. S., Ph.D. George Mason U)

"You blow it, and you blow it big! Since you seem to have difficulty grasping the basic principle at work here, I'll explain ... There is enough mathematical illiteracy in this country, and we don't need the world's highest I.Q. propagting more. Shame!" (S.S., Ph.D., U of Florida)

"Your answer to the question is in error. But if it is any consolation, many of my academic colleagues have also been stumped by this problem." (B. P, Ph.D., California Faculty Association)

After a second column, more letters:

"You made a mistake, but look at the bright side. If all those Ph.D.'s were wrong, the country would be in some very serious trouble." (Everett Harman, Ph.D., U.S. Army Research Institute).

And the column goes on to explain this for 2 more weeks, with more letters pouring in from over the country.

Post-mortem: "...[this puzzle] is particularly interesting precisely because of its specificity, its reproducibility, and its immunity to higher education."

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