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Remember, when using equally likely outcomes |A|/|S| assumes that the items counted for A are also in the sample space S. In this case, for example, to determine the Probability of getting a sum of (say) 4 includes the rolls (1,3), (2,2), and (3,1). These three "successes" from the 36 possible ordered pairs gives P(4) = 3/36. Similarly,
P(5) = |dice rolls with a sum of 5|/36 = |(1,4), (2,3), (3,2), (4,1)| / 36 = 4/36.
Continue in this manner to determine the other possibilities and then compare to the experimental sage cell seen earlier for the sum of two dice.
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