Page 1 PROBABILLITY 271 File Name : C:\Computer Station\Maths-IX\Chapter\Chap-15\Chap-15 (02-01-2006).PM65 CHAPTER 15 PROBABILITY It is remarkable that a science, which began with the consideration of games of chance, should be elevated to the rank of the most important subject of human knowledge. â€”Pierre Simon Laplace 15.1 Introduction In everyday life, we come across statements such as (1) It will probably rain today. (2) I doubt that he will pass the test. (3) Most probably, Kavita will stand first in the annual examination. (4) Chances are high that the prices of diesel will go up. (5) There is a 50-50 chance of India winning a toss in todayâ€™s match. The words â€˜probablyâ€™, â€˜doubtâ€™, â€˜most probablyâ€™, â€˜chancesâ€™, etc., used in the statements above involve an element of uncertainty. For example, in (1), â€˜probably rainâ€™ will mean it may rain or may not rain today. We are predicting rain today based on our past experience when it rained under similar conditions. Similar predictions are also made in other cases listed in (2) to (5). The uncertainty of â€˜probablyâ€™ etc can be measured numerically by means of â€˜probabilityâ€™ in many cases. Though probability started with gambling, it has been used extensively in the fields of Physical Sciences, Commerce, Biological Sciences, Medical Sciences, Weather Forecasting, etc. Page 2 PROBABILLITY 271 File Name : C:\Computer Station\Maths-IX\Chapter\Chap-15\Chap-15 (02-01-2006).PM65 CHAPTER 15 PROBABILITY It is remarkable that a science, which began with the consideration of games of chance, should be elevated to the rank of the most important subject of human knowledge. â€”Pierre Simon Laplace 15.1 Introduction In everyday life, we come across statements such as (1) It will probably rain today. (2) I doubt that he will pass the test. (3) Most probably, Kavita will stand first in the annual examination. (4) Chances are high that the prices of diesel will go up. (5) There is a 50-50 chance of India winning a toss in todayâ€™s match. The words â€˜probablyâ€™, â€˜doubtâ€™, â€˜most probablyâ€™, â€˜chancesâ€™, etc., used in the statements above involve an element of uncertainty. For example, in (1), â€˜probably rainâ€™ will mean it may rain or may not rain today. We are predicting rain today based on our past experience when it rained under similar conditions. Similar predictions are also made in other cases listed in (2) to (5). The uncertainty of â€˜probablyâ€™ etc can be measured numerically by means of â€˜probabilityâ€™ in many cases. Though probability started with gambling, it has been used extensively in the fields of Physical Sciences, Commerce, Biological Sciences, Medical Sciences, Weather Forecasting, etc. 272 MATHEMA TICS File Name : C:\Computer Station\Maths-IX\Chapter\Chap-15\Chap-15 (02-01-2006).PM65 15.2 Probability â€“ an Experimental Approach The concept of probability developed in a very strange manner. In 1654, a gambler Chevalier de Mere, approached the well-known 17th century French philosopher and mathematician Blaise Pascal regarding certain dice problems. Pascal became interested in these problems, studied them and discussed them with another French mathematician, Pierre de Fermat. Both Pascal and Fermat solved the problems independently. This work was the beginning of Probability Theory. The first book on the subject was written by the Italian mathematician, J.Cardan (1501â€“1576). The title of the book was â€˜Book on Games of Chanceâ€™ (Liber de Ludo Aleae), published in 1663. Notable contributions were also made by mathematicians J. Bernoulli (1654â€“1705), P . Laplace (1749â€“1827), A.A. Markov (1856â€“1922) and A.N. Kolmogorov (born 1903). In earlier classes, you have had a glimpse of probability when you performed experiments like tossing of coins, throwing of dice, etc., and observed their outcomes. You will now learn to measure the chance of occurrence of a particular outcome in an experiment. Activity 1 : (i) Take any coin, toss it ten times and note down the number of times a head and a tail come up. Record your observations in the form of the following table Table 15.1 Number of times Number of times Number of times the coin is tossed head comes up tail comes up 10 â€” â€” Write down the values of the following fractions: Number of times a head comes up Total number of times the coin is tossed and Number of times a tail comes up Total number of times the coin is tossed Blaise Pascal (1623â€“1662) Fig. 15.1 Pierre de Fermat (1601â€“1665) Fig. 15.2Read More

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