The probability that a customer at a grocery store pays for their items with a credit or debit card (event C) is .78. The probability that the grocery bill for a customer is greater than $100 (event H) is .37. The probability that a customer pays with a credit or debit card given that his or her grocery bill was greater than $100 is .95.

(a) What is the probability that a customer pays with a credit or debit card and his or her grocery bill was greater than $100?

(b) What is the probability that a customer’s grocery bill was over $100 given that he or she paid with a credit or debit card?

(c) In this problem, are C and H independent? Explain.