An electronics company purchases a particular component from two sources: "Supplier A" and "Supplier B". The following statistics were gathered by testing a large number of the components to see if they worked properly: 

1% of all components from Supplier A failed.

2% of all components from Supplier B failed.

After combining all components from these two suppliers in a large bin, the probability of randomly selecting a non-working component from Supplier A was 0.1%.

Answer these questions and show all of your work:

1. Given that a component did not fail, what is the probability that it came from Supplier A?

2. Given that a component failed, what is the probability that it came from Supplier B?

3. What is the ratio of the # failed components from Supplier B to the # failed components from Supplier A?