Table 10.1 is a PivotTable of Apple Purchase History showing the cross-tabulation of counts between the first purchase and the second purchase, as in Table 10.1 below (also see Fig. 5.5, p.182). Table 10.1. PivotTable. Counts of cross-tabulation between 1st purchase and 2nd purchase First Purchase Second Purchase Grand total iMac iPad iPhone iPod MacBook iMac 2 3 2 6 13 iPad 1 1 2 10 14 iPhone 3 4 14 21 42 iPod 3 12 12 30 57 MacBook 8 16 26 24 74 Grand total 15 34 42 42 67 200 (1) Divide each number in Table 10.1 by the grand total 200, we have the following table (fill up Table 9.2): Table 10.2. Joint Probabilities and Marginal Probabilities First Purchase Second Purchase Grand total iMac iPad iPhone iPod MacBook iMac iPad iPhone iPod MacBook Grand total (2) Use the data in Table 10.1, calculate the following conditional probabilities (show your calculations): (a) P(2nd purchase is MacBook | 1st purchase is iMAC) = (b) P(2nd purchase is iMAC | 1st purchase is MacBook) = (c) P(2nd purchase is iPhone | 1st purchase is MacBook) (d) P(1st purchase is iPhone | 2nd purchase is iPod) (e) P(1st purchase