The random chance that you’re right

In October 2011, Raymond Johnson in Colorado posted: “I found this on my office chalkboard this morning, thanks to +Ryan Grover. Attempt to reason through it if you must.”

As a math teacher I made some changes to the question. Originally, Ryan Grover put 60% in the list, but I erased the 6 so that option C now says 0%. There is a chance that a random choice is wrong, and let us also allow for this statistically (for more draws). I also inserted the condition that you must choose from the given list. This should be obvious to students doing multiple choice questions, but one reader on Johnson’s page (Rob Elliot) suggested that 0% was the right answer but not in the list. Thus, those loopholes are closed by including 0% in the list and restricting the choices to those in the list.

Thus, do the test:

Adapted from Ryan Grover and Raymond Grover (October 2011)

The Grover / Johnson question was picked up by more people on the internet. I myself found it on the Dutch economendagboek just now in 2014,  who referred to the interesting website by Filip Spagnoli, who referred to Cheap Talk (Jeff Ely and Sandeep Baliga), who finally led me to Grover / Johnson as the source. It was also featured by Modeled behavior, who referred to Greg Mankiw, who referred to Nathan Yau who again referred to Grover / Johnson.

Once you have your answer, you might want to check with those links and the answers provided there, keeping in mind that I adapted the question a bit (essentially helping you).

You are asked a question on probability and statistics, but never forget that you are reasoning, so that this is also an issue of logic. You are likely to benefit from my book A Logic of Exceptions(In general also economic decision making would benefit from some logic.)

It would be improper to give the answer just like that. It is vertically flipped over and you have to do some work to find it. If you are 100% sure there actually is no need to check it.


Answer to above question, flipped vertically


NB 1. I have considered to include 100% too since we want that students doing a test can feel that they can be 100% accurate. Adapting the percentages we get the following. I have not presented this in the above as the first and only example, since we want to relate to the other weblogs.

In this case, we feel the temptation that an answer to a multiple choice test should have a 100% chance of being right. So what option do you select ?

Now with 100%

Now with 100% – Adapted from Ryan Grover and Raymond Grover (October 2011)

NB 2. Raymond Johnson wrote a later review when this pop quiz went viral. He also links to an earlier version on from May 2010 that actually had the 0 % in there too.


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