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502
become probability used in Statistics.
Example: 1 It is an example with respect to attribute assuming that the effect of substance, space and time on the experiment is negligiable. Any coin with two different faces will satisfy the first three divisions but for the fourth one we have to repeat the experiment of observing any face for a finite number of times. The quantitative form of Avakatvya is the probability of getting any face, which lies between zero and unity. The probability of getting both the faces at a time or none of them is zero because the occurrence of the faces is independent. For a fair coin the probability of observing any face is half when the experiment is repeated for a finite number of times.
Example 2: It is an example with respect to substance assuming that the effect of space, time and attribute is negligible. A bag contains identical pieces of gold and silver and let the number be 'm' and 'n' respectively. The first three divisions of Syadvada are true with respect to either gold or silver. For the fourth division we have to draw a piece at random. The outcome of the draw may be a gold piece or silver piece. This uncertainty can be expressed in quantitative form which may be either m/(m+n) or n/(m+n), for gold and silver pieces respectively.
Example 3 It is an example with respect to attribute, the effect of substance, space and time is negligible on the experiment. Let us consider two identical coins with head on one face and tail on the other side. Let the occurrence of HH is Syadasti then the non occurrence of HH/(Occurrence of HT, TH,TT) is Syadnsasti. The repetition of the experiment for a finite number of times gives the probability of HH which is nothing but the quantitative form of syadavaktvya. For a fair coin this probability is 1/4.
Example: 4 It is an example of two objects each one is having two attributes. The effect of space and time is negligible on the experiment. Consider a coin with Prob. (H) p and Prob. (T) = 1-p, Now there are two urns containing m, & m, white balls and n, & n, black balls respectively. The coin is tossed and if H turns, then draw a ball from Urn 1 otherwise from Urn 2 Let E be the event that the ball drawn is white. Now the event E is Avaktvya from two points namely (i) Coin and (ii) Urn. The white ball can come from either urn and is Syadasti and the non-occurrence of white ball is Syadnasti. But the occurrence of a white ball is not a sure event and therefore it is an avaktvya or probability. If the result of the tossing of the coin is known then the probability of getting a white ball from Urn 1 is and from Urn 2 is which are conditional probabilities. Similarly other conditional probabilities can be explained.
4. Range of Probability and Conculusions:
Let p represent the quantitative measure of syadavaktvya with respect to either substance or attribute or both then the seven divisions of Syadvada are given as under.
