# Probability teaser

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[PLAIN]http://chzdailywhat.files.wordpress.com/2011/10/0b666cba-9278-4ab2-8794-46160e3b24c7.jpg [Broken]

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none of the answers is correct.

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Part of my brain thinks it's a trick question. What does it mean to be 'correct'?

What is the question?

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I ... don't know...

I can't actually reformulate it...

I like Serena
Homework Helper
I'm missing the answer 0%. ;)

There is a 50% chance you will choose 25% and a 25% chance you will choose 50%.

The correct answer is (A) and you have a 25% chance of getting it right.

A & D are the same answer, so the chances of "25%" being the correct answer is 50%, which contradicts their stated probabilities, so neither can be right.

That leaves B & C, and so since both are equally probable, means B is the only right answer

Gold Member
A & D are the same answer, so the chances of "25%" being the correct answer is 50%, which contradicts their stated probabilities, so neither can be right.

That leaves B & C, and so since both are equally probable, means B is the only right answer
so... if I randomly choose from the four answers, there is a 50% chance I will choose B?

It can either be A&D or B.

If one chooses at random, then there's a 50% probability to pick either A or D. Only B offers the choice of 50%. Thus there's a 25% chance of picking B and thus A&D are correct.

though correct me if I'm wrong, i'm about to pass out due to tiredness.

I like Serena
Homework Helper
I choose <A| + <D|.
Quantum mechanically speaking this is correct ("bra-ket" notation).

BobG
Homework Helper
It will take me 2 seconds to answer that question.

We don't actually know the question, so we can't know the answer. It is asking what is the probability of choosing the correct answer, not what the actual answer is. There are three different answers, so chosen at random wouldn't you have a 33% chance of being correct?

EDIT: Looking back at it I realize it probably isn't that simple. But it sounded good at the time.

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None

assumptions:
-"random" means our choice is a uniformly distributed random variable
-the problem can have at most one correct answer even if it is stated by many possible choices
(for example, the answer can't be both 50% and 25% but it can be both A and D)

(attempt at a) solution:
*Let's suppose that A is the correct answer.
Then D is the correct answer also, since they state the same thing.

Therefore, the chance of hitting a correct answer is .5. Therefore, B is the correct answer which is contradictory. So A can't be the correct answer.

*Under the same reasoning, D can't be the correct answer

*Let's suppose B is the correct answer.
Thus the chance of hitting a(the) correct answer is .25. Thus A or D is the correct answer, which is contradictory.

*same goes with C

Therefore none of the above answers is correct.

That was fun! (or might still be if I got it wrong!)

Are my assumptions wrong?
Is the solution wrong?

Hats off to Constantinos. My head exploded!

BobG
Homework Helper
*Let's suppose that A is the correct answer.
Then D is the correct answer also, since they state the same thing.

Are my assumptions wrong?
Is the solution wrong?

This assumption is incorrect. For example, take questions #6 and #17 of this test. B/D and D/B would seem to be correct answers for both questions, but there is only one correct answer for each question.

You need the entire test to know for sure whether A or D (or both) is the correct answer. Depending on the context, a random choice could still have only a 25% chance of being correct, even when two choices list the same answer - and even if there's not enough information provided to know which choice listing 25% is the correct answer.

Edit: However, there does have to be some assumption made in order for there to be a correct answer. For example, there are 26 letters in the English alphabet, 28 in the Spanish alphabet, and 33 in the Cyrillic alphabet. Since the question is written in English, assuming they're talking about picking a random letter in the English alphabet would be a good assumption - except picking a random letter would have less than a 25% chance of being correct - meaning there must be some other limiting assumptions made, as well.

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Admittedly, although they specify "random", they don't actually specify that the randomness is evenly distributed. It could be random with a bias, in which case it's not possible to determine the answer, despite the fact that there might be a correct one.

DaveE

BobG
Homework Helper
Forensic analysis indicates the correct answer must be A.

All of the numbers except one were written by the same person. The handwriting style of the '2' in answer D is different than the handwriting style used for the other numbers.

Additionally, most of the erasure marks on the board match the circular motion used to erase a large amount of data. The almost straight line erasure mark coming from the '2' in answer D indicates a very small amount of data was erased while taking care not to erase other data.

Furthermore, proper testwriting technique requires the choices to be written in some sort of logical order: shortest to longest, longest to shortest, smallest to largest, etc. A, B, and C are properly formatted with each answer giving a higher percentage, and then D suddenly presents a lower percentage. D clearly was originally 65%, 75%, 85%, or 95%.