In a game of tossing two dice, for example, the total number of possible outcomes is 36 (each of six sides of one die combined with each of six sides of the other), and the number of ways to make, say, a seven is six (made by throwing 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, or 6 and 1) therefore, the probability of throwing a seven is 6/ 36, or 1/ 6. But this holds only in situations governed by chance alone. The probability of a favourable outcome among all possibilities can be expressed: probability ( p) equals the total number of favourable outcomes ( f) divided by the total number of possibilities ( t), or p = f/ t. It is the ratios that are accurately predictable, not the individual events or precise totals. The law of large numbers is an expression of the fact that the ratios predicted by probability statements are increasingly accurate as the number of events increases, but the absolute number of outcomes of a particular type departs from expectation with increasing frequency as the number of repetitions increases. Probability statements apply in practice to a long series of events but not to individual ones. In games of pure chance, each instance is a completely independent one that is, each play has the same probability as each of the others of producing a given outcome.
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