A cross-tabulation of sales transactions data is shown to the right. Use the data to complete parts a Region and b below. Book DVD Total East 51 48 99 North 44 48 92 South 64 39 103 West 105 92 197 Total 264 227 491 a. Find the marginal probabilities that a sale originated in each of the four regions and the marginal probability of each type of sale (book or DVD). The marginal probability for the eastern region is The marginal probability for the northern region is The marginal probability for the southern region is The marginal probability for the western region is The marginal probability for book sales is The marginal probability for DVD sales is | (Round to three decimal places as needed.) b. Find the conditional probabilities of selling a book given that the customer resides in each region. The conditional probability for book sales given residence in the eastern region is The conditional probability for book sales given residence in the northern region is The conditional probability for book sales given residence in the southern region is The conditional probability for book sales given residence in the western region is (Round to three decimal places as needed.)