Banks providing loans Banks are providing loans. 

While granting a loan two scenarios can take place


The Loan is repaid
The Loan is not-repaid


The benefit from a re-payed loan is small profit. (Let's say 5% in general)
The loss from a not re-payed loan is huge loss. (you lost all your investments)

Are there formulas that can calculate the ratio of loss of (based on pseudo-numbers for example) or other theories related to this issue?
If you have an estimate of the probabilities of each scenario, say with probability $p\in[0,1]$ the loan is repaid (assuming no other scenario exists), then you can calculate the expected value of making the loan of size $L$: 


In scenario 1, payoff is $-L+(1+0.05)L=0.05L$ (giving out $L$ and getting back the principal plus interest)
In scenario 2, payoff is $-L$ (giving out $L$ and getting nothing back)


The expected payoff from making the loan would be 
\begin{equation}
EV=p(0.05)L+(1-p)(-L)=1.05pL-L.
\end{equation}