What is the probability of solving 500 random questions correctly?

[ahmedhassan72]

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

 

[Gib Z]

This seems more like homework than a riddle...

 

[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)

 

[Gib Z]

Yes, its correct.