Probability Teaser Puzzle - Challenge Your Mind

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In summary, the conversation discusses a multiple choice question with four possible answers, where the correct answer is unknown. The participants try to determine the probability of choosing the correct answer at random and discuss various assumptions and possibilities. However, it is ultimately concluded that the question cannot be answered without creating contradictions.
  • #1
DaveC426913
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[PLAIN]http://chzdailywhat.files.wordpress.com/2011/10/0b666cba-9278-4ab2-8794-46160e3b24c7.jpg [Broken]
 
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  • #2
none of the answers is correct.
 
  • #3
Part of my brain thinks it's a trick question. What does it mean to be 'correct'?
 
  • #4
What is the question?
 
  • #5
I ... don't know...

I can't actually reformulate it...
 
  • #6
I'm missing the answer 0%. ;)
 
  • #7
my head hurts
 
  • #8
There is a 50% chance you will choose 25% and a 25% chance you will choose 50%.

So...60% is my final answer.
 
  • #9
The correct answer is (A) and you have a 25% chance of getting it right.
 
  • #10
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
 
  • #11
regor60 said:
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?
 
  • #12
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.
 
  • #13
I choose <A| + <D|.
Quantum mechanically speaking this is correct ("bra-ket" notation).
 
  • #14
It will take me 2 seconds to answer that question.
 
  • #15
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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  • #16
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?
 
  • #17
Hats off to Constantinos. My head exploded!
 
  • #18
Constantinos said:
*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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  • #19
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
 
  • #20
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%.

Answer D was altered to maliciously mislead the masses.
 
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  • #21
Like Constantinos, showed, its unanswerable.
There are lots of questions that can't be answered without creating contradiction.
For eg.
Answer in Yes or No, Will your answer be 'No' ?
 

What is a probability teaser puzzle?

A probability teaser puzzle is a type of brain teaser that involves using mathematical probability to solve a problem or puzzle. It challenges individuals to think critically and creatively to find the most logical and accurate solution.

How do you solve a probability teaser puzzle?

The first step in solving a probability teaser puzzle is to clearly define the problem and understand the given information. Then, you can use mathematical formulas and logical reasoning to calculate the probability of different outcomes. It may also help to visualize the problem or create a diagram to better understand the situation.

What skills can be developed by solving probability teaser puzzles?

Solving probability teaser puzzles can help develop critical thinking, problem-solving, and analytical skills. It also requires individuals to think outside the box and approach problems from different perspectives. Additionally, it can improve mathematical abilities and logical reasoning.

Are probability teaser puzzles only for mathematicians?

No, probability teaser puzzles are for anyone who enjoys a challenge and wants to exercise their brain. Although they involve mathematical concepts, they do not require advanced mathematical knowledge. Anyone can improve their skills and solve these puzzles with practice and determination.

Where can I find more probability teaser puzzles to solve?

There are many resources available online, such as puzzle websites and books, that offer a variety of probability teaser puzzles. You can also create your own puzzles by applying probability concepts to everyday situations or problems. Additionally, joining a puzzle-solving community or group can provide access to new and challenging puzzles.

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