Probablity

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Page 4 :INTRODUCTION
Definition:
Probability is the study of chance or the likelihood of an event happening. Directly or indirectly, probability plays a role in all activities. Probability is a measure or estimation of how likely it is that something will happen or that a statement is true. Probabilities are given a value between 0 (0% chance or will not happen) and 1 (100% chance or will happen). The higher the degree of probability, the more likely the event is to happen, or, in a longer series of samples, the greater the number of times such event is expected to happen. In its simplest form, probability can be expressed mathematically as: the number of occurrences of a targeted event divided by the number of occurrences plus the number of failures of occurrences (this adds up to the total of possible outcomes): p(a) = p(a)/[p(a) + p(b)]

Calculating probabilities in a situation like a coin toss is straightforward, because the outcomes are mutually exclusive: either one event or the other must occur. Each coin toss is an independent event; 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 (50-50). History:

Concepts of probability have been around for thousands of years, but probability theory did not arise as a branch of mathematics until the mid-seventeenth century. Probability theory had its start in the 17th century, when two French mathematicians, Blaise Pascal and Pierre de Fermat carried on a correspondence discussing mathematical problems dealing with games of chance. Contemporary applications of probability theory run the gamut of human inquiry, and include aspects of computer programming, astrophysics, music, weather prediction, and medicine. PAGE 5 :

Application of Probability in various fields:
Aristotle said, "The probable is what usually happens." We can't predict the future, but we can use mathematical probability to determine how likely it is that something will or won't happen. People often use probability to make better choices in their lives. Knowing the probability of a certain event happening or not happening can be very important to us in the real world. Weather Forecasting

Suppose we have some outdoor plans made for a particular day and the weather report says that the chance of rain is 70%. Should we still go ahead with your plans or should we cancel them for another day? Where this forecast does comes from? Meteorologist are able to calculate the likelihood of what the weather may be on a particular day by looking back in a historical database and examining all the other days in the past that had the same weather characteristics and then determine that on 70% of those similar days it rained. The mathematical formula for probability can be used to demonstrate these findings. When looking for the chance it will rain, this will be the number of days in the database that it rained is divided by the total number of similar days. For example, if there is data for 100 days with similar weather conditions (the sample space), and on 70 of these days it rained (a favorable outcome), the probability of rain on the next similar day is 70/100 or 70%. Since a 50% probability means that an event is just as likely to happen as not to happen, a 70% chance means that it is more likely to rain than not. Therefore, perhaps it is best that we stay home and reschedule our plans for another day! Batting Average

A batting average involves calculating the probability of a player hitting the ball. The sample space is the total number of time a player has had at bat and each hit is a favorable outcome. Therefore, in 10 at-bats a player gets 3 hits, his or her batting average is 3/10 or 30%. For baseball stats, all the percentages are multiplied by 10, so a 30% probability translates to a 300 batting average. So let's say your favorite baseball player is batting 300. This means...
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