choose defaults:
chance accused is guilty after real witnesses
chance accused has friends and would tell true confession if guilty
percentage of friends who are desperate to make a deal
chance a non-inmate felon would be desperate and sophisticated enough to lie
number of potential lying felons in the timing window
chance will confess to felon if guilty:
chance of true confession if accused:
chance of fake confession:
chance of confession if guilty:
total chance of confession fake or real:
expected noncorrelated confession witnesses:
chance confession witness is lying:
p (guilty | confession) = p (confession|guilty) * p (guilty) / p (confession)
= * /