What is "theory of chances"

Chance \Chance\ (ch[.a]ns), n. [F. chance, OF. cheance, fr. LL. cadentia a allusion to the falling of the dice), fr. L. cadere to fall; akin to Skr. [,c]ad to fall, L. cedere to yield, E. cede. Cf. Cadence.]

1. A supposed material or psychical agent or mode of activity other than a force, law, or purpose; fortune; fate; -- in this sense often personified.

   It is strictly and philosophically true in nature and reason that there is no such thing as chance or accident; it being evident that these words do not signify anything really existing, anything that is truly an agent or the cause of any event; but they signify merely men's ignorance of the real and immediate cause.
   --Samuel Clark.

   Note: Many of the everyday events which people observe and attribute to chance fall into the category described by Clark, as being in practice too complex for people to easily predict, but in theory predictable if one were to know the actions of the causal agents in great detail. At the subatomic level, however, there is much evidence to support the notion derived from Heisenberg's uncertaintly principle, that phenomena occur in nature which are truly randomly determined, not merely too complex to predict or observe accurately. Such phenomena, however, are observed only with one or a very small number of subatomic particles. When the probabilities of observed events are determined by the behavior of aggregates of millions of particles, the variations due to such quantum indeterminacy becomes so small as to be unobservable even over billions of repetitions, and may therefore be ignored in practical situations; such variations are so improbable that it would be irrational to condition anything of consequence upon the occurrence of such an improbable event. A clever experimenter, nevertheless, may contrive a system where a very visible event (such as the dynamiting of a building) depends on the occurrence of a truly chance subatomic event (such as the disintegration of a single radioactive nucleus). In such a contrived situation, one may accurately speak of an event determined by chance, in the sense of a random occurrence completely unpredictable, at least as to time.

   Any society into which chance might throw him.
   --Macaulay.

   That power Which erring men call Chance.
   --Milton.

2. The operation or activity of such agent.

   By chance a priest came down that way.
   --Luke x. 31.

3. The supposed effect of such an agent; something that befalls, as the result of unknown or unconsidered forces; the issue of uncertain conditions; an event not calculated upon; an unexpected occurrence; a happening; accident; fortuity; casualty.

   In the field of observation, chance favors only the mind that is prepared.
   --Louis Pasteur.

   Note: This quotation is usually found in the form "Chance favors the prepared mind." It is a common rejoinder to the assertion that a scientist was "lucky" to have made some particular discovery because of unanticipated factors. A related quotation, from the Nobel-Prize-winning chemist R. B. Woodward, is that "A scientist has to work wery hard to get to the point where he can be lucky."

   It was a chance that happened to us.
   --1 Sam. vi. 9.

   The Knave of Diamonds tries his wily arts, And wins (O shameful chance!) the Queen of Hearts.
   --Pope.

   I spake of most disastrous chance.
   --Shak.

4. A possibility; a likelihood; an opportunity; -- with reference to a doubtful result; as, a chance to escape; a chance for life; the chances are all against him.

   So weary with disasters, tugged with fortune. That I would get my life on any chance, To mend it, or be rid on 't
   --Shak.

5. (Math.) Probability.

   Note: The mathematical expression, of a chance is the ratio of frequency with which an event happens in the long run. If an event may happen in a ways and may fail in b ways, and each of these a + b ways is equally likely, the chance, or probability, that the event will happen is measured by the fraction a/a + b, and the chance, or probability, that it will fail is measured by b/a + b.

   Chance comer, one who comes unexpectedly.

   The last chance, the sole remaining ground of hope.

   The main chance, the chief opportunity; that upon which reliance is had, esp. self-interest.

   Theory of chances, Doctrine of chances (Math.), that branch of mathematics which treats of the probability of the occurrence of particular events, as the fall of dice in given positions.

   To mind one's chances, to take advantage of every circumstance; to seize every opportunity.