A manufacturing firm has two suppliers for an electrical component used in its process: one in Mexico and one in China. The supplier in Mexico ships 82% of all the electrical components used by the firm and has a defect rate of 4%. The Chinese supplier ships 18% of the electrical components used by the firm and has a defect rate of 6%.
a. Calculate the probability that an electrical component is defective.
b. Suppose an electrical component is defective. What is the probability that component was shipped from Mexico?