A liquor store owner is willing to cash personal checks for amounts up to $50, but she has become wary of customers who wear sunglasses. Fifty percent of checks written by persons wearing sunglasses...

Extracted text: A liquor store owner is willing to cash personal checks for amounts up to $50, but she has become wary of customers who wear sunglasses. Fifty percent of checks written by persons wearing sunglasses bounce. In contrast, 98% of the checks written by persons not wearing sunglasses clear the bank. She estimates that 10% of her customers wear sunglasses. If the bank returns a check and marks it "insufficient funds," what is the probability that it was written by someone wearing sunglasses?