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Example 1.15 Flip four coins, a penny, a nickel, a dime, and a quarter. Examine the coins in order (penny, then nickel, then dime, then quarter) and observe whether each coin shows a head (h) or a tail (t). What is the sample space? How many elements are in the sample space? The sample space consists of 16 four-letter words, with each letter either h or t. For example, the outcome tthhrefers to the penny and the nickel showing tails and the dime and quarter showing heads. There are 16 members of the sample space. 1.5 PARTITIONS AND THE LAW OF TOTAL PROBABILITY 19 A B, B. B C, Figure 1.1 In this example of Theorem 1.8, the partition is B = {B1, B2, B3, B4} and Ci = An Bi for i = 1, . .., 4. It should be apparent that A = C1 UC2 UC's UC4