Example 4-1. Suppose that a product is produced in three factories X, Y and Z. It is known that factory X produces thrice as many items as factory Y, and that factories Y and Z produce the same number...

Extracted text: Example 4-1. Suppose that a product is produced in three factories X, Y and Z. It is known that factory X produces thrice as many items as factory Y, and that factories Y and Z produce the same number of items: Assume that it is known that 3 per cent of the items produced by each of the factories X and Z are defective while 5 per cent of those nanufactured by factory Y are defective. All the itenis produced in the three factories are stocked, and an item of product is selected at randoni. (i) What is the probability that this item is defective ? (ii) If an item selected at randoı is found to be defective, what is the probability that it was produced by factory X, Y and Z respectively ?