Probability of Production Machine A

A factory produces two types of widgets, Type I and Type II. The production ratio of Type I to Type II is 3:2. The factory has two machines: Machine A and Machine B.

Machine A produces 60% of Type I widgets and 40% of Type II widgets, while Machine B produces 40% of Type I widgets and 60% of Type II widgets.

If a randomly selected widget from the factory is known to be Type I, what is the probability that it was produced by Machine A?