11. In Example 3.21 in Chapter 3, we developed the following cross-tabulation of sales transaction data:

Region Book DVD Total East 56 42 98 North 43 42 85 South 62 37 99 West 100 90 190 Total 261 211 472

a. Find the probabilities that a sale originated in each of the four regions and the probability of each type of sale (book or DVD).

b. Find the conditional probabilities of selling a book given that the customer resides in each region.