So since we have our CNN acting as a pre-filter we can reduce the \(FAR\) of any system by using the multiplication rule of probability, making the value to be \(\left(1-\frac{94}{100}\right)\) which is the probability that the CNN falsely accepts a fake fingerprint multiplied by \(x\) which is the \(FAR\) of any system.
Therefore, \(FAR^{new}=FAR\cdot\left(1-\frac{94}{100}\right)\ =\ 0.06\ \cdot\ FAR\)
Let us take experimental results from our K- nearest neighbour algorithm, We computed the \(FAR\) to be 0.026 and the \(FNAR\) to be 0. Similar accuracy can be found in multiple minutiae matching algorithms like for example in the mentioned citation. \cite{r2009}
So, the resulting \(FAR\ =\ 0.026\) will be improved as \(FAR^{new}=0.026\cdot0.06\ =\ 0.00156\)