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Q: The ratio of the number of ways an event can occur to the number of ways the event cannot occur?

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That defines the odds in favour of the event.

If each of the ways is equally likely then it is the probability of the event but otherwise it is simply a ratio.

experimental probability

An irrational number is a real number that cannot be expressed as a ratio of two integers.

The probability of the event occurring.

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That defines the odds in favour of the event.

The term is probability (theoretical probability), or how likely a given event is to occur.

If each of the ways is equally likely then it is the probability of the event but otherwise it is simply a ratio.

number of outcomes divided by the number of ways of occurrence

There is no single word. It is the "probability of that event" (four words).

the extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible

the extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible

A number that cannot be expressed as the ratio of two integers is known as an irrational number.

the measure of how likely an event is to occur Probability refers to the extent to which a given event is likely to appear. It is usually measured by the ratio of the favorable cases to the whole number of cases possible.

odds"The odds against an event is a ratio of the probability that the event will fail to occur (failure) to the probability that the event will occur (success). To find odds you must first know or determine the probability of success and the probability of failure.Odds against event = P(event fails to occur)/P(event occurs) = P(failure)/P(success)The odds in favor of an event are expressed as a ratio of the probability that the event will occur to the probability that the event will fail to occur.Odds in favor of event = P(event occurs)/P(event fails to occur) = P(success)/P(failure)"Allen R. Angel, Christine D. Abbott, Dennis C. Runde. A Survey of Mathematics with Applications. Pearson Custom Publishing 2009. Pages 286-288.

An irrational number is a number that cannot be written as a ratio of two numbers.

experimental probability

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