Sparking widgets

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 bayes ex­traor­di­nary claims.