The table below indicates the probabilities of various outcomes with regard to the size of purchases and method of payment for customers that enter to a large New York electronics store:

a. Is the event of a customer paying cash independent of the event that the customer spends \(

b. Given that the customer pays cash, what is the probability that the customer spends \(\leq \$ 500\) ?

c. Given that the customer pays by credit card, what is the probability that the customer spends \(\leq \$ 500\) ?

d. What is the probability that the customer pays by credit card, given that the purchase is \(\leq \$ 500\) ?

e. Given that the customer spends \(\$ 100\) or more, what is the probability that the customer will not pay by cash?

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Size of purchase $500 Method of payment Credit card Layaway plan Cash .20 .10 .15 .15 .05 .20 .01 .05 .09