A factory produces two types of widgets: Type A and Type B. The probability of producing a Type A widget is 0.4, while the probability of producing a Type B widget is 0.6. Each Type A widget has a 20% chance of being defective, and each Type B widget has a 10% chance of being defective.
If a randomly selected widget from the factory is defective, what is the probability that it is a Type A widget?