Question

A light bulb manufacturer knows that 0.07% of all bulbs manufactured are defective. A testing machine is 98% effective. If a randomly selected light bulb is tested and found to be defective, what is the probability that it actually is defective?

Answer 1

 P[ actually defective & shown as defective] = 98% of 0.08% = 0.0784% 
P[ok & shown as defective] = 2% of 99.92% = 1.9984% 

P[actually defective | shown as defective] = 0.0784/(0.0784+1.9984) = 3.775% <-------