Probability of positivity of rational solutions to a diophantine system?

Pick integers $a,b,c,d$ uniformly and randomly on conditions $a,b,c,d>0$, $ad+bc<2max(ac,bd)$, $ac<bd<(1+delta)^2ac$ at a fixed $delta>0$ (perhaps bigger than $1$) and $min(a,b,c,d)>max(m,n)$ where $t<m,n<2t$ holds and $m,n$ are coprime integers and $t>0$.

There are $m’,n’inmathbb Q$ such that
$$m=m’a+n’b$$
$$n=m’c+n’d$$
holds with $|m’|,|n’|<1$ with probability $1-o(1)$ since $ad-bc$ is $neq0$ and is arbitrary with probability $1-o(1)$.

I have a very simple question. I think only 1. has a chance of being true and has probability $1/3$. However how to show it?

1. What is the probability that $0<m’n'<1$ together with $0<n'<m'<1$ holds (both solutions have same signs and positive)?

2. What is the probability that $0<m’n'<1$ together with $0<m'<n'<1$ holds (both solutions have same signs and positive)?

Are these equiprobable (that is with probability $1/6$ each) or only 1. has a chance and thus probability of 1. is $1/3$?

If not are they bounded away from $0$ in some sense?