A liquor store owner is willing to cash personal checks for the amounts up to $50, but she has become wary of customers wearing sunglasses. Fifty percent of checks written through persons wearing sunglasses bounce. In contrast, 98% of checks written by persons not wearing sunglasses clear the bank. She determines that 10% of here customers wear sunglasses.
(a) Find out the probability that the bank returns the checks and marks it "insufficient funds".
(b) If the bank returns the checks and marks it "insufficient funds", determine the probability that it is written by someone wearing sunglasses?