9. A Blum-Blum-Shub random number generator produces a string of random bits. A bit is random if the probability of it being 0 or 1 is 1/2. Let’s assume a random bit number is generated (that is, a binary string of length n).
(10 points)
What is the probability that a string with all 1’s is generated?
What is the probability that a string with 1’s is generated?

Question

9. A Blum-Blum-Shub random number generator produces a string of random bits. A bit is random if the probability of it being 0 or 1 is 1/2. Let’s assume a random  bit number is generated (that is, a binary string of length n).
(10 points)
What is the probability that a string with all 1’s is generated?
What is the probability that a string with  1’s is generated?

anonymous · Answer

a)Probability of all 1´s =0.5^n
b)probability of all 0´s is 0.5^n--->probability at least one "1" =1-0.5^n