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Has Marilyn Done It Again?

Marilyn vos Savant, owner of the world's highest IQ according to Guiness Record Books, has possibly put her foot where it should not go....You decide!

In a recent column, Marilyn responded to the following question:

Say you plan to roll a die 20 times. which of these results is more likely:

(a) 11111111111111111111, or
(b) 66234441536125563152?

And Marilyn's "possible-foot-in-mouth" response: In theory, the results are equally likely. Both specify the number that must appear each time the die is rolled. (For example, the 10th number in the frist series muts be a 1. the 10th number in the second series must be a 3.) Each number--1 through 6-- has the same chance of landing faceup.

But let's say you tossed a die out of my view and then said that the results were one of the above. Which series is more likely to be the one you threw? Because the roll has already occurred, the answer is (b). It's far more likely that the roll produced a mixed bunch of numbers than a series of 1's.

So, is she right...or wrong? I "no" my vote...but will let you argue over it.


Source: "Ask Marilyn," Parade Magazine, July 31, 2011

Hint: Reduce the question to a simpler form...you flip a coin twice. Are the sequences HH and HT equally likely? Remember that order is important, as the sequence HT is different from the sequence TH.


Solution Commentary: Some side comments...

First, it has nothing to do with the fact that the rolls have occurred. The probability of these two distinct events remain equal.

Second, Marilyn seems to be confusing the situation with the question...If you roll a die 20 times, is it more likely that you will get a stringt of all 1's or a string of a variety of numbers 1-6? This is not the same question!

In Parade (10/23/2011), math teacher George Alland argued that Marilyn was incorrect withy clear examples...but Marilyn refused to budge (e.g. "she said "My answer is correct.").