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Result 3 Let E. E... Ebe K mutually exclusive and collectively exhaustive events, and let A be some other event. Then the K events En A, E, A Ex nA are mutually exclusive, and their union is A--that is, (ERATUIE, NATUULEX OA) - A 13.18) We can better understand the third statement by examining the Venn diagram in Fig. ure 3.12. The large rectangle indicates the entire sample space and is divided into smaller rectangles depicting K mutually exclusive and collectively exhaustive events EE The event A is represented by the closed figure. We see that the events composed of the intersection of A and each of the events are indeed mutually exclusive and that their union is simply the event A. We can therefore, write the following E MAULE AU UKENDA) = A 124 Chapter 3 Probability 25 E E EE EX Figure 3.12 Venn Diagram for Result 3 AEnAEnAEnAEnAEnA ENA A Example 3.27 Single Die (Results 1 and 2) Consider a die-rolling experiment with A = (2, 4, 6 and B = (4,5,6). Show the following a. (ANB) U (ANB) = 8