What is the probability of solving 500 random questions correctly?

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Discussion Overview

The discussion revolves around the probability of correctly answering 500 random questions when the answers are unknown, framed as a riddle or homework problem. Participants explore the mathematical reasoning behind calculating this probability.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents a method to calculate the probability, suggesting that the total number of combinations for answering 500 questions is 2^500, leading to a derived probability of answering all correctly as approximately 0.3054936364 * 10^-148 percent.
  • Another participant expresses skepticism about the nature of the problem, implying it resembles a homework question rather than a riddle.
  • A later reply confirms the initial calculation as correct, although it is noted that the original solver expressed uncertainty about the accuracy of their solution.

Areas of Agreement / Disagreement

While one participant agrees with the calculation presented, there is an underlying skepticism about the framing of the problem as a riddle versus a homework question. The discussion does not reach a consensus on the nature of the problem.

Contextual Notes

The calculation relies on assumptions about the independence of question answers and does not address potential limitations in the approach or the implications of the extremely low probability derived.

ahmedhassan72
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Solve my simple riddle!

If you have 500 questions (put right or wrong questions) and you will solve them all randomly as you don't know the answer so what is your probability to solve them all right?
express answer as e.g 1.5*10^-2
 
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This seems more like homework than a riddle...
 
If you have 500 questions (put right or wrong questions) and you will solve them all randomly as you don't know the answer so what is your probability to solve them all right?
express answer as e.g 1.5*10^-2
( don't think to try combinations one by one)
You can easily solve that 2 right or wrong questions have 2 answer probabilities, 3 right or wrong or wrong questions have 8 answer probabilities , and so on... so the number of combinations which you can get =number of one question probabilities ^number of questions
so 500 questions combinations = 2^500 ( can't be solved by most calculators)
so let 2^500 =x
so log 2^500 = log x
so 500log 2 =log x
so x=10^(500log2)
=10^150.5149978
=10^150 * 10^5149978
=3.273390608 * 10^150
probability of solving them all right = 1/(3.273390608* 10^150) *100 =
=======0.3054936364 * 10 ^-148 percent
( i imagined of that problem and i solved it so it may be wrong)
 
Last edited:
Yes, its correct.
 

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