Suppose that 30 percent of the bottles produced in a certain plant are defective. If a bottle is defective, the probability is 0.9 that an inspector will notice it and remove it from the filling line. If a bottle is not defective, the probability is 0.2 that the inspector will think that it is defective and remove it from the filling line.

a) If a bottle is removed from the filling line, what is the probability that it is defective?

b) If a customer buys a bottle that has not been removed from the filling line, what is the probability that it is defective.

 http://www.bilkent.edu.tr/~math250/Solution%20set2.pdf