# Suppose we use the family F of functions described in Section 3.8.5, where there is a 20% chance of.

Suppose we use the family F of functions described in Section 3.8.5, where there is a 20% chance of a minutia in an grid square, an 80% chance of a second copy of a fingerprint having a minutia in a grid square where the first copy does, and each function in F being formed from three grid squares. In Example 3.23, we constructed family F1 by using the OR construction on 1024 members of F. Suppose we instead used family F2 that is a 2048-way OR of members of F. (a) Compute the rates of false positives and false negatives for F2. (b) How do these rates compare with what we get if we
Suppose we use the family F of functions described in Section 3.8.5, where there is a 20% chance of a minutia in an grid square, an 80% chance of a second copy of a fingerprint having a minutia in a grid square where the first copy does, and each function in F being formed from three grid squares. In Example 3.23, we constructed family F1 by using the OR construction on 1024 members of F. Suppose we instead used family F2 that is a 2048-way OR of members of F. (a) Compute the rates of false positives and false negatives for F2. (b) How do these rates compare with what we get if we organize the same 2048 functions into a 2-way AND of members of F1, as was discussed at the end of Section 3.8.5?