\(FAR^{Fake-NonEnrolled}=FAR_{fd}\cdot FAR_{iv}\) (for an attacker trying to be authenticated using a fake reproduction of a finger which is not the enrolled one)
\(FAR^{Fake-Enrolled}=FAR_{fd}\cdot\gamma\) (for an attacker trying to be authenticated using a fake reproduction of the enrolled finger)
where \(\gamma\ <\ \left(1-FRR_{iv}\right)\) since, even if a fake fingerprint is created by using professional equipments, its quality is usually lower than the real finger it is designed to imitate and therefore the chance that the identity verification algorithm does not match it with the user’s real template is higher