[Solved by Experts] Factory X Supplies 60

Problem 2 (Week 15; Bayes Rule to evaluate Product / Operations Reliability)   

Suppose that  It is known that factory X supplies 60% of the total bulbs available and Y supplies 40% of the total bulbs available.  

1)What is the chance that a purchased bulb will work forever? 

2)Given that a purchased bulb will work forever, what is the chance that it was made in Factory X?