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)

= * /