A department store analyzed its most recent sales and determined the relationship between the way the customer paid for the item and the price category of the item. The joint probabilities in the following table were calculated: Size of Purchase Method of Payment Cash Credit Card Debit Card Under $20 0.09 0.03 $20 - $100 0.05 0.21 Over $100 0.03 0.23 a) What proportion of purchases was paid by debit card? b) Find the probability of an over $100 purchase given that it is a credit card purchase. c) Determine the proportion of purchases made by credit card or debit card. d) Are the events "payment by cash" and "purchase of under $20" mutually exclusive? Explain. e) Are the events "payment by cash" and "purchase of under $20" independent? Explain.
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A department store analyzed its most recent sales and determined the relationship between the way a customer paid for an item and the price category of the item. The joint probabilities are given in the table below: Cash Credit Card Debit Card Under 20 Dollars 0.11 0.02 0.03 20-100 Dollars 0.05 0.2 0.17 Over 100 Dollars 0.01 0.26 0.15 A. What proportion of purchases were paid with a debit card? Proportion = B. Find the probability that a purchase was over 100 dollars given that it is a credit card purchase. Probability = C. Determine the proportion of purchases made by credit card or debit card. Proportion =
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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? (Round your answer to 4 decimal places.) (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? (Round your answer to 4 decimal places.) (c) In this problem, are C and H independent? Yes No
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