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## Suppose a nut fall from a tree at time 'T1'. There are so many activities influenced to fall the nut from the trees at time 'T1'. These activities cause by so many reasons during a long time span. It can be a bird who drops the seed at time T2, rain fall at time durations T3 to T3, someone feeds manure at time 'T4' and all these cause to grow the tree to this height and the blow of wind at time T6 caused the nut to fall down at time 'T1'. If these are the only effects on the tree and its environment, this is the only way the nut can fall on ground and there are no any other ways it can happen.

This is the absolute possibility, valid universally on all our activities from beginning of the universe and in future.

Similarly we can deduce that all our activities are governed by the nature and other influences around us are destined to happen. Aware of this these circumstances if we change our cause of action it is also another influence. We are just obeying the rules set forth upon us by other forces acting upon us from our birth until now. The course of events is predefined and we cannot escape the irresistible power.

From the beginning of universe until now this course of action depended on progress of unidirectional time. Also effect each power source can be resolved in to two components that are independent of each other. Such power source include attractive and repulsive forces between two bodies, heat, light, exra terrestrial forces, divine forces, acoustic forces, mental forces etc. If we indicate this effect graphically we can show it as shown in this figure.

When we expect a result, we primarily define a number of choices for the result. for example when we toss a dice we primarily propose it 6 choices as as possibilities. For the dice, our choices or expected results are 1,2,3,4,5, and 6. When we throw it universal time Tx the effect of Ux and Uy result on our dice and it results the absolute possibility of outcome. But if we throw the dice at Ty it will be a different result.

Probability indicates the extent to which an event is likely to occur. Possibility is the universal set whereas probability is the subset. Possibility is surer to occur than probability. Probability is a theory whereas possibility is a happening. Happenings have to combine together to make probability a possibility. There will be no probability without possibility, but possibility without probability.

## The probabilities in a situation like a coin toss the outcomes are mutually exclusive: either one event or the other must occur. Each coin toss is an

independentevent; the outcome of one trial has no effect on subsequent ones. No matter how many consecutive times one side lands facing up, the probability that it will do so at the next toss is always .5.

The sample space for the experiment is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.

As we can see from the above chart we can get 2 results possible after the 1st toss. After the second toss we are getting 4 possible results and after the third toss we are getting 8 possible outcomes. Probability of getting head after 3 tosses, probabilities of getting head alone is 1/8.

Probability Vs. PossibilityProbability is the mathematical chance that an event will happen, and it is expressed as a percentage or a fraction, Probability is not the same as possibility.

Therefore we can write

## Probability = Number of events produced by a given out come / Total number of possibilities

## Baye's Rule

The

of an eventconditional probabilityBis the probability that the event will occur given the knowledge that an eventAhas already occurred. This probability is writtenP(B|A), notation for theprobability of B given A. In the case where eventsAandBareindependent(where eventAhas no effect on the probability of eventB), the conditional probability of eventBgiven eventAis simply the probability of eventB, that isP(B).

If eventsAandBare not independent, then the probability of theintersection of A and B(the probability that both events occur) is defined by

P(A and B) = P(A)P(B|A).

From this definition, the conditional probabilityP(B|A)is easily obtained by dividing byP(A):

To calculate the probability of the intersection of more than two events, the conditional probabilities ofallof the preceding events must be considered. In the case of three events,A,B, andC, the probability of the intersectionP(A and B and C) = P(A)P(B|A)P(C|A and B).

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`Last edited : On 7th October 2010 by Leelananda Jayasuriya. `