**Probability**

History

The scientific study of probability is a modern development. Gambling shows that there has been an interest in quantifying the ideas of probability for millennium, but exact mathematical descriptions arose much later. There are reasons of course, for the slow development of the mathematics of probability. Whereas games of chance provided the impetus for the mathematical study of probability, fundamental issues are still obscured by the superstitions of gamblers.

According to Richard Jeffrey, "Before the middle of the seventeenth century, the term 'probable' meant approveable, and was applied in that sense, univocally, to opinion and to action.

Probability in Casinos

The mathematics of gambling are a collection of probability applications encountered in games of chance and can be included in game theory. From mathematical point of view, the games of chance are experiments generating various types of aleatory events, the probability of which can be calculated by using the properties of probability on a finite space of events. Now we can take the example of Roulette for learning about the payout. The Roulette disk contains 38 spaces; 18 red spaces, 18 black spaces and 2 green spaces numbered 0 & 00. If we place a bet on number 5 and spin, then the payout will be 1:35 i.e if we place a bet of five dollars then the winning amount will be 1/35=5/x therefore x=$175. But the payout ratios vary with probability of a category of numbers occurring.

Probability in Lottery

People often misunderstand the notion of independent events. This is a probability term meaning that past events have no influence on future outcomes. When flipping a coin, the probability of getting a head does not change no matter how many times you flip the coin. When the coin is flipped and the first three flips are heads, the fourth flip still has the probability of ½. However, many people misunderstand that the first three flips somehow influence the fourth flip, but they do not. The probability is still the same, as if the first three flips had never occurred. if a person picked 36 as one of their numbers and one of the drawn numbers was 35, it does not really imply that the person was close to winning. Although 35 and 36 are only one number apart, it does not mean that after 35 was picked, 36 would be the next number. In fact, the person is no closer than if 3 or 97 were picked. People often think this way, but it is just a misconception of independent events.

Probability in Predicting Weather

The probability information is typically derived by using several numerical model runs, with slightly varying initial conditions. This technique is usually referred to as ensemble forecasting by an Ensemble Prediction System (EPS). EPS does not produce a full forecast probability distribution over all possible events, and it is possible to use purely statistical or hybrid statistical/numerical methods to do this. For example, temperature can take on a theoretically infinite number of possible values (events); a statistical method would produce a distribution assigning a probability value to every possible temperature. Impossibly high or low temperatures would then have close to zero probability values.

Introduction

Probability is a measure or estimation of likelihood of occurrence of an event. 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.

When dealing with experiments that are random and well-defined in a purely theoretical setting (like tossing a fair coin), probabilities describe the statistical number of outcomes considered divided by the number of all outcomes (tossing a fair coin twice will yield head-head with probability 1/4, because the four outcomes head-head, head-tails, tails-head and tails-tails are equally likely to occur). When it comes to practical application, however, the word probability does not have a singular direct definition.

**Group 1**

Graphical Representation

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