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- Muhammad Ali

Chapter

16

PROBABILITY

Where a mathematical reasoning can be had, it is as great a folly to make use of any other, as to grope for a thing in the dark, when you have a candle in your hand. – JOHN ARBUTHNOT

16.1 Introduction

© no N C tt E o R be T re pu

an even number in throwing a die as

3 1 i.e., . Here the 6 2

In earlier classes, we studied about the concept of probability as a measure of uncertainty of various phenomenon. We have obtained the probability of getting

total possible outcomes are 1,2,3,4,5 and 6 (six in number). The outcomes in favour of the event of ‘getting an even number’ are 2,4,6 (i.e., three in number). In general, to obtain the probability of an event, we find the ratio of the number of outcomes favourable to the event, to the total Kolmogorov number of equally likely outcomes. This theory of probability (1903-1987) is known as classical theory of probability. In Class IX, we learnt to find the probability on the basis of observations and collected data. This is called statistical approach of probability. Both the theories have some serious difficulties. For instance, these theories can not be applied to the activities/experiments which have infinite number of outcomes. In classical theory we assume all the outcomes to be equally likely. Recall that the outcomes are called equally likely when we have no reason to believe that one is more likely to occur than the other. In other words, we assume that all outcomes have equal chance (probability) to occur. Thus, to define probability, we used equally likely or equally probable outcomes. This is logically not a correct definition. Thus, another theory of probability was developed by A.N. Kolmogorov, a Russian mathematician, in 1933. He

bl is he

384

MATHEMATICS

laid down some axioms to interpret probability, in his book ‘Foundation of Probability’ published in 1933. In this Chapter, we will study about this approach called axiomatic approach of probability. To...

16

PROBABILITY

Where a mathematical reasoning can be had, it is as great a folly to make use of any other, as to grope for a thing in the dark, when you have a candle in your hand. – JOHN ARBUTHNOT

16.1 Introduction

© no N C tt E o R be T re pu

an even number in throwing a die as

3 1 i.e., . Here the 6 2

In earlier classes, we studied about the concept of probability as a measure of uncertainty of various phenomenon. We have obtained the probability of getting

total possible outcomes are 1,2,3,4,5 and 6 (six in number). The outcomes in favour of the event of ‘getting an even number’ are 2,4,6 (i.e., three in number). In general, to obtain the probability of an event, we find the ratio of the number of outcomes favourable to the event, to the total Kolmogorov number of equally likely outcomes. This theory of probability (1903-1987) is known as classical theory of probability. In Class IX, we learnt to find the probability on the basis of observations and collected data. This is called statistical approach of probability. Both the theories have some serious difficulties. For instance, these theories can not be applied to the activities/experiments which have infinite number of outcomes. In classical theory we assume all the outcomes to be equally likely. Recall that the outcomes are called equally likely when we have no reason to believe that one is more likely to occur than the other. In other words, we assume that all outcomes have equal chance (probability) to occur. Thus, to define probability, we used equally likely or equally probable outcomes. This is logically not a correct definition. Thus, another theory of probability was developed by A.N. Kolmogorov, a Russian mathematician, in 1933. He

bl is he

384

MATHEMATICS

laid down some axioms to interpret probability, in his book ‘Foundation of Probability’ published in 1933. In this Chapter, we will study about this approach called axiomatic approach of probability. To...

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