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These pairs correspond to outcomes of an experiment

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Unformatted text preview: course, it is reasonable that P (T ) = 1/2, because T takes up half of the area of the square. In fact, any reasonable subset of the square is an event, and the probability of any event A is the area of A. 1.3 Calculating the size of various sets An important class of probability spaces are those such that the set of outcomes, Ω, is ﬁnite, and all | outcomes have equal probability. Therefore, the probability for any event A is P (A) = |A| , where |Ω |A| is the number of elements in A and |Ω| is the number of elements in Ω. Thus, it is important to be able to count the number of elements in various sets. Such counting problems are the topic of this section. Principle of counting Often we are faced with ﬁnding the number of vectors or sets satisfying certain conditions. For example, we might want to ﬁnd the number of pairs of the form (X,N) such that X ∈ {H, T } and N ∈ {1, 2, 3, 4, 5, 6}. These pairs correspond to outcomes of an experiment, in which a coin is ﬂipped and a...
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