A manufacturing company produces a widget that comes in two types which are A and B. 33% of the widgets produced are type A and 67% are type B. The widgets also come in three sizes. Not accounting for...

A manufacturing company produces a widget that comes in two types which are A and B. 33% of the widgets produced are type A and 67% are type B. The widgets also come in three sizes. Not accounting for widget type, the company produces 20% of widgets in size 1, 45% of widgets in size 2, and 35% of widgets in size 3. If somebody pulls a widget for quality testing from the production facility, which is the probability that the widget is type A or size 2? Also the probability of any widget being both type A and size 2 is 0.16. Is the event of type A and the event of size 2 mutually exclusive or not?