Sparking widgets

by Nate Soares Jul 6 2016

10% of widgets are bad and 90% are good. 4% of good widgets emit sparks, and 12% of bad widgets emit sparks. If a widget is sparking, find an easy way to calculate the chance that it's a bad widget, keeping the operations as simple as possible so that it's easy to do the calculation entirely in your head.

You're encouraged to solve the problem yourself without looking at the answer. an answer can be found in Extraordinary claims require extraordinary evidence.