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If you choose an answer to this question at random, what is the chance you will be correct?

A) $25\%$

B) $50\%$

C) $60\%$

D) $25\%$

https://plus.google.com/+RaymondJohnson/posts/CSXeyftovTJ

Michael Hardy
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  • http://math.stackexchange.com/questions/76491/multiple-choice-question-about-the-probability-of-a-random-answer-to-itself-bein?rq=1, the accepted answer. – peterwhy Jul 12 '15 at 01:22
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    The canonical question has "C) 0%", but earlier askings with "C) 60%" have been closed as duplicates too (here and here, as well as several now deleted ones), after a chat discussion concluded that 76491 should be extended to cover that too. – hmakholm left over Monica Jul 12 '15 at 01:35

2 Answers2

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Rob Elliot answered this succintly:

There is no ball in this option. The questions asks. If you choose an answer to this question at random, what is the chance you will be correct.

It's not asking. If you choose an answer to this question at random, which of the answers represents the chance in percent you will be correct.

Lets rephrase the question.

If you choose an answer to this question at random, what is the chance you will select a fruit?

  • A) Mushroom
  • B) Potato
  • C) Carrot
  • D) Mushroom

The question isn't tied to the answer being the only option. the wording of it is asking to calculate the chance of the out come independently of the provided answers.

Thus

  • A) 25%
  • B) 50%
  • C) 60%
  • D) 25%

If the Answer is 25%. There would have to be a 25% chance that you will select an answer of 25%. Because there are two options of 25% A and D there is a great statistical chance you will select an answer of 25%, thus neither is the correct answer.

If the Answer is 50%. There would have to be a 50% chance you would select an answer equal to 50%. There is only one option of 50% and thus a lower Statistical chance you will select it and thus it is also incorrect.

if the Answer is 60% you would have to have more then 4 options thus the answer is in correct.

There for A, B, C, and D are all incorrect to the chance, and there for the chance of you selecting the correct answer from one of those 4 options is 0%

Community
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yuritsuki
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  • This is of course assuming that a) b) c) & d) all have an equal probability of being chosen. There are many different ways to randomly choose something. – Zach L Jul 12 '15 at 01:25
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The problem here is that the answer you choose affects the question. Here is my two cents:

There is no correct answer, so the question is invalid.

If the answer is A or D, then the answer is 25% percent. However the chance of guessing right is then 50%, so the answer is B, a contradiction.

If the answer is B, then the answer is 50%, but the chance of guessing B is 25%, so the answer is A or D, a contradiction.

If the answer is C, then the answer is 60%, but again the chance of guessing right is 25%, so the answer is A or D.

Every choice leads to a contradiction. I believe this makes the question a paradox.

pancini
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