Suppose you generate an $N$-bit string (composed of only $1$'s and $0$'s). The sum of all of these $0$'s and $1$'s is $X$.
- What is the probability that $X$ is odd, if $N$ is odd?
- What is the probability that $X$ is odd, if $N$ is even?
Since the chance of any bit being a $0$ or $1$ is $50\%$, I would just assume that both answers are $50\%$. However, I don't think this is quite right. Can I get some ideas on how to solve this problem? Any help would be greatly appreciated.