Solve 500 Right or Wrong Questions: 0.3054936364*10^-148% Probability

[ahmedhassan72]

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)

 

[arildno]

Quite right you are!

Have you covered this in school yet, or is maths also a hobby for you?

 

[ahmedhassan72]

no i a haven't covered it in school that riddle is mine and maths is my best hobby

 

[HallsofIvy]

You are assuming that in "answering them all randomly" you have a 50-50 chance of getting anyone correct. That would be true only in "True-False" questions. If each question were multiple choice with 5 possible answers, the probability of answering one correctly by choosing at random would be 0.2 and the probability of answering them all correctly would be (0.2)⁵⁰⁰. If the questions were "essay" type, there is no way of figuring the probability of answering anyone of them correctly.

 

[arildno]

But, ahmedhassan DID make the assumption of (right or wrong) questions at the start.
Although I agree that this is ambiguous (since 4 wrongs and 1 right might be called a "right and wrong"-question!), I gave him the benefit of doubt.

 

[HallsofIvy]

One of these days I really should learn to read.