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The misconception of representativeness arises from a misconception about the nature of randomness.  When considering the random selection of a certain number of events from a given sample space, it seems very likely that the events chosen will be from "all over" the sample space.  Similarly, it seems very unlikely that the selection will consist only of a "piece" of the sample space.  For example, suppose you are randomly selecting letters of the alphabet to make a new word.  The word is to have three letters and each letter of the word is to be chosen from all 26 letters of the alphabet.  Is it more likely that you will come up with the "word" kte than the "word" zzz?  Let’s look at the probabilities behind each:

kte :

The probability that k will be the first letter of your word is 1/26. 

The probability that t will be the second letter of your word is 1/26. 

The probability that e will be the third letter of your word is 1/26. 

As a result, the probability that each of these letters will be chosen in that order is 1/26 * 1/26 * 1/26 = approximately .00006

zzz :

The probability that z will be the first letter of your word is 1/26. 

Because the second letter can be chosen from any of the 26 letters of the alphabet, including z, the probability that z will be the second letter of your word is still 1/26. 

Again, because the third letter can be chosen from any of the 26 letters of the alphabet, including z, the probability that z will be the third letter of your word is 1/26 .

As a result, the probability that each of these letters will be chosen in that order is also 1/26 * 1/26 * 1/26 = approximately .00006.

Thus, even though selections without patterns seem "more random" than selections with patterns, if the trials are independent and all events are equally likely, the two types of selections are equally likely.

*Link to the Lucky Number Lesson Plan that addresses this misconception.