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Unformatted text preview: there are other events. For example, we might deﬁne B to be the event that the number that
shows is two or smaller. Equivalently, B = {1, 2}. Since B has two outcomes, it’s reasonable that
P (B ) = 2/6 = 1/3. And E could be the event that the number that shows is even, so E = {2, 4, 6},
and P (E ) = 3/6 = 1/2.
Starting with two events, such as B and E just considered, we can describe more events using
“and” and “or,” where “and” corresponds to the intersection of events, and “or” corresponds to
the union of events. This gives rise to the following two events1 :
“the number that shows is two or smaller and even ” = BE = {1, 2} ∩ {2, 4, 6} = {2} “the number that shows is two or smaller or even” = B ∪ E = {1, 2} ∪ {2, 4, 6} = {1, 2, 4, 6}.
The probabilities of these events are P (BE ) = 1/6 and P (B ∪ E ) = 4/6 = 2/3. Let O be the event
that the number that shows is odd, or O = {1, 3, 5}. Then:
“the number that shows is even and odd” = EO = {2, 4, 6} ∩ {1, 3, 5} = ∅ “the number that shows is even or odd”...
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 Spring '08
 Zahrn
 The Land

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