Probablity
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
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