Please answer the following:

5. Costco buys masks from three dierent rms: Firm B (45%), lm G (10%), and rm S (45%). In the past, Costco found that 2% of rm B's masks are faulty, and 5% of rm GS and rm S's masks are faulty. A customer buys mask without looking at the rm's name. When she gets home, she nds the mask is faulty. What is the probability that she chose rm B's mask? [8 marks]