Please help me to answer following question with necessary steps
One detergent Company has two production facilities, one in "abc" and the other one in "xyz". The company makes the same type of detergent at both facilities. The "abc" plant makes 60% of the company's total output and the "xyz" plant 40%.
All detergent from the two facilities is sent to a central warehouse, where it is intermingled. After extensive study, the quality assurance manager has determined that 5% of the detergent produced in "abc" and 10% of produced in "xyz" is unusable due to quality problems. When the company sells a defective product, it incurs not only the cost of replacing the item but also the loss of goodwill. The vice president for production would like to allocate these costs fairly between the two plants. To do so, he knows he must first determine the probability that a defective item was produced by a particular production line. Specifically, he needs to answer these questions:
1. What is the probability that the detergent was produced at the "abc" plant, given that the soap is defective?
2. What is the probability that the detergent was produced at the "xyz" plant, given that the soap is defective?