Probability

Probability represents the ratio of favourable cases to the total number of all cases. In other words, it is a measure of uncertainty regarding an event. The more uncertain an event is, the lower its probability. The probability of an event is determined by calculating the ratio of favourable cases to total cases. The total number of cases is known as the sample space. If a formula is known as a random variable, we can find its probability. The formula of probability is used in various fields to estimate the chances of an event occurring.

Concept of probability:

Probability is a measure of the uncertainty in an event. It refers to the chance of a particular outcome in an experiment and how likely it is. It can be calculated by finding out how often a person has experienced favourable events compared to all possible outcomes of an event. 

Probability meaning in literal terms: A problem that may be solved by calculus.

The formula of Probability = Number of favourable cases/ Total number of all cases.

Types of probability:

Probability can be classified into two types:

1. Subjective probability
2. Objective probability

Subjective probability:

P(A) means the probability of event A. In this probability, we assume the event is not certain, and all possible outcomes are equally likely. 

The formula of subjective probability is as follows:

P(A)= probability of A without knowing the outcome.

For example: Suppose on a highway, you come across two exits. The probability of choosing exit A is higher than or equal to 50% while choosing B exit is lower than 50%. In this case, the probability of choosing A is higher. However, in other cases, if we do not know that the outcome will be favourable or unfavourable, then our choice will be based on subjective probability, i.e. in such cases, our decision is based on what seems logical (based on all options).

Objective probability:

In the case of objective probability, we consider the outcome of an event and its knowledge. 

The formula for objective probability is as follows:

P(A)=average P(A|B). It can also be written as P(AB), where A is the event and B is the event’s outcome.

Suppose many people are given a job. In this case, getting a job depends on many factors, like education, experience, etc. Taking these into consideration gives us a different number for objective probability. 

For example: Suppose 50 people can apply for job A (a new position). If we consider knowledge regarding the person’s outcome getting selected for this position, i.e. B, then 50 persons can apply for this job. The probability of getting selected is lower than 50%, while the other person’s probability of getting selected is equal to or higher than 50%. In this situation, it is evident that person B has a higher probability of getting selected than person A.

The above example concludes that subjective and objective probabilities cannot be compared without knowing the knowledge regarding the outcome. 

Uses and applications of probability:

The formula of probability is used in various fields. The study of probability enables us to plan our strategies based on the outcome of events. Probability helps in understanding the nature of future events (predicting the future), for example, the bankruptcy of a bank, the rate of growth of population etc. The study of probability also helps in minimising the loss. For example, it is used in the insurance and betting industries, where insurance companies use probability to calculate the premium, and bettors use it to win money by making predictions on an uncertain outcome.

Some of the probability questions’ examples are:

• If a dice is rolled, what is the probability of getting a number greater than 4?

Ans. The probability of getting a number greater than 4 is 16.

• Suppose a fair coin is tossed. What is the probability of rolling heads?

Ans. The probability of rolling heads is 12.

• If a die is rolled, a number from 1 to 8 is obtained. The die was rolled three times more than the number on the previous roll. Find the probability of getting 1, 3 or 5 on the next roll.

Ans. The probability of getting 1, 3 or 5 on the next roll is 16 because if we are to get a number from 1 to 6 in total, then its probability is one (1), three (3) and five (5) for getting a number.

Conclusion: 

The theory of probability is the study of the uncertainty of an event. The formula of probability is used in various fields such as insurance, betting, weather forecasting etc.

There are two types of probability, objective probability and subjective probability. If a theory is based on objective probabilities, then it can be tested, whereas if it is based on subjective probabilities, it cannot be tested because of uncertainty. (Theories are always based on objective probabilities.) A great number of phenomena in nature possess a random character. The study of such phenomena is called ‘Probability’.