## Probability Measure

Let us return to the Texas lotto example. The odds, or probability, of winning are 1 /N for each valid combination rnj of six numbers; hence, if you play n different valid number combinations {«jl, …,Mjn}, the probability of winning is n/N:P({«^,}) = n/N. Thus, in the Texas lotto case the probability P(A), A e &, is given by the number n of elements in the set A divided by the total number N of elements in ^. In particular we have P(Q) = 1, and if you do not play at all the probability of winning is zero: P(0) = 0.

The function P(A), A e &, is called a probability measure. It assigns a number P(A) e [0, 1] to each set A e &. Not every function that assigns numbers in [0,1] to the sets in & is a probability measure except as set forth in the following definition:

Definition 1...

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