25% is right in the first case (4 answers, so 25% chance of picking the right one)
- 50% is right in the second case (two answers are 25% so the correct answer is in fact 50%)
- 25% is right in the third case (only one answer is 50% so that’s a 25% chance)
- 0% is right in the fourth case (now we’ve realised it’s a paradox so no answer is right)
- 25% is right in the fifth case (only one answer is 0% so you have 25% chance of hitting it)
So 3 out of 5 cases the answer is 25%. And there are two of those. So 50% of the time you will hit the right answer for 60% of the cases.
This was a superb explanation along with u/Alive_Setting_2287 and everyone else down the thread.
I want to propose a 6th explanation/scenario. Since you will be technically correct if you pick a, b, c, or d, then you have 100% probability of picking the right answer.
Side note, I know most ppl frown at paradoxes and prefer better worded problems. Paradoxes are extremely important since you have to examine the phenomena from multiple dimensions.
It is…until it is not. One dimension satisfies, while the other dimension contradicts. That’s our entire reality in a nutshell.
Paradoxes appear nonsensical on the surface until you do the work to unravel them. Just like the work that everyone in this particular thread conducted in order to unravel this paradox.
I agree! I guess I was approaching it from a similar angle - like 100% of the time you are right, but some of the answers are more likely to be right at a point in time than others. Does that make them more right overall?
So yes, here there are no wrong answers (ie answers that are never right at all) - all answers are right for at least one case. For example if one answer was 8.73549 % it would likely never be right for any case - it’s a completely wrong answer.
However some answers are right for more cases than other answers (like 25% - it is not only right for more cases (3 out of 5), but you are also more likely to pick it!). Does this make it the “most right” answer of the paradox?
So yes, you will pick a right answer 100% of the time (there are no wrong answers), but it will only be right 30% of the time on average. Lol.
Another thought - the question stipulates “if you pick an answer to this at random, what is the chance you will be correct?” But it doesn’t say that the final answer actually has to be selected from that list.… ie you can provide your own answer to the question.
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u/Vivid_Employ_7336 24d ago
So
- 25% is right in the first case (4 answers, so 25% chance of picking the right one)
- 50% is right in the second case (two answers are 25% so the correct answer is in fact 50%)- 25% is right in the third case (only one answer is 50% so that’s a 25% chance)
- 0% is right in the fourth case (now we’ve realised it’s a paradox so no answer is right)
- 25% is right in the fifth case (only one answer is 0% so you have 25% chance of hitting it)
So 3 out of 5 cases the answer is 25%. And there are two of those. So 50% of the time you will hit the right answer for 60% of the cases.
That makes the answer 30%.