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CHANCE AND PROBABILITY.

In calculating the probability of any event, the difficulty is not, as many persons imagine, in the process, but in the statement of the proposition, and the great trouble with many of those who dispute on questions of chance is that they are unable to think clearly.

The chance is either for or against the event; the probability is always for it. The chances are expressed by the fraction of this probability, the denominator being the total number of events possible, and the numerator the number of events favourable. For instance: The probability of throwing an ace with one cast of a single die is expressed by the fraction ⅙; because six different numbers may be thrown, and they are all equally probable, but only one of them would be an ace. Odds are found by deducting the favourable events from the total, or the numerator from the denominator. In the example, the odds against throwing an ace are therefore 5 to 1. The greater the odds against any event the more improbable it is said to be, and the more hazardous it is to risk anything upon it.