2. An online bookstore sells both print books and e-books (books in an electronic format). Customers can pay with either a gift
card or a credit card. a. Suppose that the probability of the event "print book is purchased" is 0.6 and that the probability of the event "customer pays using gift card" is 0.2. If these two events are
independent, what is the probability that a randomly selected book purchase is a print book paid for using a gift card?
b. Suppose that the probability of the event "e-book is purchased" is 0.4; the probability of the event "customer pays using gift card" is 0.2; and the probability of the event "e-book is
purchased and customer pays using a gift card" is 0.1. Are the two events "e-book is purchased" and "customer pays using a gift card" independent? Explain why or why not.
a. The two events mentioned here are " print book is purchases" and "customer using gift card". P(P)=0.6 and P(C)=0.2. we have to calculate the probability of print book selection for purchase and payment is made through gift card i.e. P(P∩C). P(P∩C)=P(P)*P(C)=0.6*0.2=0.12.
b. If P(A∩B)=P(A)*P(B), then the two events are independent. Here in the given situation two independent variables are "purchase of e-book" and "payment made using gift card"
P(E)=0.4
P(G)=0.2
P(E and G)=P(E∩G)=0.1
P(E)*P(G)=0.4*0.2=0.08 that is not equal to 0.1. So, the two events "e-book is purchased" and "Payment made by customer using gift card" are not independent.
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