NFA Semantics

Suppose we make a probabilistic process out of an NFA N as follows. At any given point at the computation, the NFA is in some state p and sees some letter a$.$ If there are no a$-$arrows out of p$,$ N goes into a death state, reads the rest of the string, and rejects. If there is one a$-$arrow out of p$,$ then N takes it$.$ If there are more than one a$-$arrow, it takes the first arrow $($alphabetically$)$ with probability $1/2,$ the next with probability $1/4,$ the next with probability $1/8,$ and so on$,$ except that the last two arrows have the same probability. Then for any input string w$,$ w is in L$($N$)$ if and only if the probability that this process accepts, on input w$,$ is greater than $0.$ true or false