# Simple riddle!

## Main Question or Discussion Point

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?????????
( 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
Homework Helper
Gold Member
Dearly Missed
Quite right you are!

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

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

HallsofIvy
Homework Helper
You are assuming that in "answering them all randomly" you have a 50-50 chance of getting any one 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 any one of them correctly.

arildno
Homework Helper
Gold Member
Dearly Missed
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