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Unformatted text preview: st of rolling two fair dice, and deﬁne the following three
events about the numbers showing: A =“sum is even,” B =“sum is a multiple of three,” and
C =“the numbers are the same.” Display the outcomes in a threeevent Karnaugh map, and ﬁnd
P (ABC ).
Solution. We write ij for the outcome such that i appears on the ﬁrst die and j appears on the
second die. The outcomes are displayed in a Karnaugh map in Figure 1.3. It is a little tedious to ﬁll
in the map, but it is pretty simple to check correctness of the map. For correctness it suﬃces that
for each of the events A, Ac , B, B c , C, C c , the correct outcomes appear in the corresponding lines
(rows or columns). For example, all 18 outcomes in A are in the bottom row of the map. All 18
outcomes of Ac are in the upper row of the map. Similarly we can check for B, B c , C, and C c . There
are 36 elements in Ω, and ABC = {33, 66}, which has two outcomes. So P (ABC ) = 2/36 = 1/18. Example 1.4.3 Suppose a deck of playing cards has 52 cards, represented by the set C :
C = {1C, 2C,...
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 Spring '08
 Zahrn
 The Land

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