A retail shop manager analyzed the relationship between sales and the method of payments. Based on his analysis, he has produced the following joint probability table, as shown below: Size of purchase Method of payment Cash Credit card Debit Card Under $20 0.09 0.03 0.04 $20 -$100 0.05 0.21 0.18 Over $100 0.03 0.23 0.14 a. What proportion of purchases were paid by debit card? (2 marks) b. What proportion of purchases were paid by cash? (2 marks) c. Determine the proportion of purchases made by credit card or by debit card? (2 marks) d. Are the events "payment by cash" and "purchase of under $20" mutually exclusive? Explain your answer.