Note that now 1h is not the same thing as in the

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Unformatted text preview: nt so that we don't keep track of which coin is which, but only how many give heads; elem events now are 0H (same as 2T), 1H (same outcome as 1T), and 2H (same as 0T); events include "at least one head" (which now is {1H, 2H}), etc. Note that now 1H is not the same thing as in the previous example; it is not a two ­element event but rather is a single elementary event.  ­ Axioms: given a sample space S, Prob (or P, or a "probability distribution") is a real ­valued function on the set of events P:Events  ­ ­> [0,1] such that for all events A,B (subsets of S) (i) P(S) = 1 (ii) if (A int B) = emptyset, then P(A u B) = P(A) + P(B)  ­ Consequences of the axioms (iii) P(S ­A) = 1  ­ P(A) (iv) P(emptyset) = 0 (v) P(A u B) = P(A) + P(B)  ­ P(A int B)  ­ Uniform prob distributions: each elem event e has the same prob...
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