A factory produces two types of items, Product X and Product Y, in batches. For Product X, there are 7 batches, and each batch contains 12 defective items and 30 non-defective items. For Product Y, there are 9 batches, and each batch contains 8 defective items and 25 non-defective items. If a randomly selected item from these batches is found to be defective, what is the probability that it is a Product X item?
