A manufacturer has two quality control inspectors independen

A manufacturer has two quality control inspectors independently check each case of products for chipped or cracked products before the cases leaving the plant. Having observed the work of the two trusted inspectors over several years, the manufacturer has determined that the probability of a defective case getting by the first inspector is 0.05 and the probability of a defective case getting by the second inspector is 0.10. What is the probability that a defective case gets by both inspectors?

Solution

As the inspectors inspect independently of each other,

P( Defective case gets by both) = P(defective case gets by first inspector) * P(defective case gets by second inspector)

= 0.05*0.10 = 0.005