In a certain factory, Machine A, Machine B, and Machine C are all producing widgets. Widgets produced by Machine A have a 1% chance of being defective. Likewise, widgets produced by Machine B and Machine C are defective 4% and 2% of the time, respectively. Of the total production of widgets in the factory, Machine A produces 30%, Machine B produces 25%, and Machine C produces 45%. Suppose a widget is selected at random from this factory.
a) What is the probability the widget is defective?
b) If the widget is defective, what is the probability it was produced by Machine B?
Any help would be appreciated. I believe that i am suppose to use the counting rule combination but am not sure because we are given two different sets of %...