Assignment:
The Positively Charged company uses capacitors from two different manufacturers. Historically, 60% of the capacitors come from manufacturer 1. While 90% of capacitors from manufacturer one pass quality-control checks, only 75% of the capacitors from manufacturer two pass the checks. A capacitor selected at random is found to be faulty. What is the probability it was from manufacturer 2?
Provide complete and step by step solution for the question and show calculations and use formulas.