You're looking at Less Wrong's discussion board. This includes all posts, including those that haven't been promoted to the front page yet. For more information, see About Less Wrong.

ThisSpaceAvailable comments on Mental Model Theory - Illusion of Possibility Example - Less Wrong Discussion

1 Post author: ScottL 18 August 2015 06:29AM

You are viewing a comment permalink. View the original post to see all comments and the full post content.

Article Navigation

Comments (2)
Tags: mental_model_theory

Comments (2)

You are viewing a single comment's thread.

Comment author: ThisSpaceAvailable 19 August 2015 04:11:54AM 1 point [-]

So, we have

  1. We don't have both “Either K or A” and “Either Q or A”
  2. Therefore, we either have “Neither K nor A” or “Neither Q nor A”
  3. Since both of the possibilities involve “no A”, there can be no A.

Your post seems to be a rather verbose way of showing something that can be shown in three lines. I guess you're trying to illustrate some larger framework, but it's rather unclear what it is or how it adds anything to the analysis, and you haven't given the reader much reason to look into it further.

The reason that someone might think an Ace would be a good choice is that they misread it as saying “one of these two statements is true”. But it is nowhere stated that either statement is true; rather it is stated that at least one statement is false. Once one notices that the Ace is involved in both of these statements, of which one has to be false, one's intuition should lead one choosing the King.

Also, if you're using set notation, (K ∪ A) indicates the same thing as (A or K or K ∩ A).

Comment author: ScottL 19 August 2015 04:34:53AM *  1 point [-]

I have rewritten the header to this post to make it clear that you should read the post in main first and only look at this one if it is required.

Technically the problem is very simple, but it does frequently fool people. If you write out the logic of it like in the above post, then people will very easily get the right answer. This post is meant to be a verbose explanation of the solution for people who don't believe that you should choose the king. You can read this post if you want to know why people get fooled by this simple problem.

This is the example as it is written in the academic literature

Only one statement about a hand of cards is true:

  1. There is a King or Ace or both.
  2. There is a Queen or Ace or both.

Which is more likely, King or Ace?

Most people say Ace.

Powered by Reddit Powered by Reddit