Les's have the next situation:
There is a system who asks for certification.
For that , the system sends you a seed of 16 bits , and you need to response with a result of 24 bit. Each time, the seed is different and uniformly.
What is the probability to keep wrong in the guess for N times, with the next algorithm:
Each time you get the seed, randomise a uniformly 24 bit value and hope for good.
What is the probability to not succeed after 100000000 (N) trials.
Is it $(1-\frac{1}{2^{24}})^N$ or $(1-\frac{1}{2^{40}})^N$ ?
For your information, a success is to give the correct response (nevertheless what is the seed)
Thanks a lot !!