A face recognition device can be set to one of three thresholds, A, B and C, with a false acceptance rate (FAR) and false rejection rate (FRR) of 1% and 0.5% for A, 0.1% and 2% for B, and 0.01% and 8% for C. For controlling entry to a laboratory, the requirement is a FAR of 0.1% or less, and within that, legitimate users should be rejected as rarely as possible. Which threshold should be chosen?

Answer: B. Threshold B

First select the settings that meet the requirement. B (0.1%) and C (0.01%) have a FAR of 0.1% or less; A (1%) would accept an impostor once in 100 attempts, so it does not meet the requirement. Next, of B and C, the one that rejects legitimate users less often has the lower FRR; B's 2% is lower than C's 8%, so B is chosen. C rejects impostors more reliably, but genuine users would be rejected about 8 times in 100, hurting usability. You can also confirm that as the threshold becomes stricter from A to C, FAR falls and FRR rises. Meeting the security requirement first as a constraint and then maximizing convenience is the basic way to set the threshold.

• A. A has a FAR of 1% and does not meet the requirement of 0.1% or less.
• B. Correct. Of B and C, which meet the FAR requirement, B has the lower FRR (2%).
• C. C also meets the FAR requirement, but its FRR of 8% is high, so legitimate users are rejected more often.