Results on Probability

Probability has been considered one of the branches of mathematics. This particular branch is concerned with the description that is numerical. This numerical description represents how likely an event has the possibility of occurrence along with its true proposition. Based on this particular fact, the current study will discuss the definition of probability. Different formulas of probability will be discussed in order to cast light on different results of probability. Besides that, the posterior probability and the solutions of different probability questions have been included in the study as well. 

Definition of probability

In simple diction, it can be stated that the probability of is a number that represents the chance of the occurrence of a particular event. Between ranges from zero to one, the proportion of the probability can be expressed. In order to represent the numerical result of probability in percentages, the numerical representation can have the ranging from 0% to 100%. As per the formulation of the representation of probability, 0 indicates no chance of occurrence of an event. On the contrary, 1 expresses the certainty of the occurrence of an event. 

Probability results of different probability formulas

In accordance with the complementary rules, the moment an event has been represented as the union of two other events, the result will be calculated as P(A or B)= P(A)+P(B)- P(A∩B). As per the conditional rule, it has been conjectured that A has already occurred and the result of the probability of the occurrence of B will be P (B∣A) = P (A∩B)/ P (A). On the basis of these results, the primary formula of the probability has been developed. The ratio of favourable outcomes and total favourable outcomes is considered the numerical representation of the prime probability formulas. Here, the term P (B) is the probability of event B whereas n(B) is the favourable outcome and n(S) represents the total number of events. 

Explanation of posterior probability of repeat result 

The posterior probability shares a close relationship with the prior probability that refers to the probability of an event that will happen before taking any new evidence into account. In simpler diction, the posterior probability refers to the probability of an event that will be numerically represented after taking all the backgrounds and the evidence into account.  In a nutshell, the posterior distribution is a summarised version of what probability one has found after the data have been observed based on a repetitive occurrence of a particular event. 

Terminology of probability theory 

In order to understand the key terms of the probability, the terminologies have been mentioned and discussed in the below section:

• The experiment has been referred to as a trial that is conducted to produce an outcome. 
• Together all the possible outcomes of the experiments are referred to as the sample space in order to calculate the probability
• The production of the desired result by an event is being recognised as the term named favourable outcomes.  
• Doing a random experiment is referred to as a trial that is an important terminology in calculating the probability. 

Explanation of questions regarding the probability 

It has been conjectured that two coins are tossed 500 times. Two heads are gotten 105 times, one head is gotten 275 times and no heads have come 120 times. Based on these events, the probability of each event occurring is needed to be found. Following the statement of the question, the events of getting one head, two heads and no head are represented by E1, E2 and E3, respectively. When the sum of all elementary events of a random experiment is 1 then the formulation of the probability will be P(E1)+P(E2)+ P(E3)= 0.21+0.55+0.24= 1

Important notes on probability

Probability most of the time has been represented as a fraction and the value lies between 0 and 1. In addition, while calculating the probability an event can be defined as the subset of simple space. On the other hand, one of the main facts regarding probability is that an experiment that is random has not been able to predict the outcomes that are exact. In a contradictory manner, it can be stated that a random experiment has the ability to offer some probable outcomes. 

Conclusion 

Based on the discussion that has been represented in the entire study, it has been seen that probability is the numerical representation of the likelihood of any occurrence. The fundamentals that underlie probability have been expressed along with the counterintuitive nature of probability. Along with including different probability results, the terminology of probability theory has been explained in a brief manner. On the other hand, it has been seen that probability has different solutions, as different rules are valid for attaining the numerical representation of the likelihood of the occurrences.