Applications of Probability: Probability is the branch of mathematics that tells the occurrence of an event. In our real life, we can see several situations where we can predict the outcomes of events in statistics. These outcomes may be specific or uncertain to occur. The formula of probability is the ratio of favourable events to the total number of events in an experiment.

The uncertainty of the event gives the probability of the event. The real-life applications of probability are many in various fields like medicines, business, and other industries also. In this article, we will provide detailed information on applications of probability. Continue reading to learn more!

What is Probability?

Probability is the special branch of statistics in mathematics, which tells about a random experiment. Probability defines the possibility. In general, many events of the experiments cannot be predicted with absolute certainty. For those cases, probability helps predict an event’s likelihood.

The measurement of the possibility of an event to occur is called probability. The uncertainty of the event gives the probability of the event.

Example:
Probably, today going to rain, winning the cricket match etc.

Formula of Probability

The formula of probability is the ratio of favourable events to the total number of events in an experiment.

\({\text{probability}}\left({{\text{Event}}} \right) = \frac{{{\text{Favourable}}\,{\text{outcomes}}}}{{{\text{Total}}\,{\text{number}}\,{\text{of}}\,{\text{outcomes}}}}\)

Probability gives the uncertainty of the occurrence of an event numerically. The probability of occurrence of an event can lie between zero and one. Where one is the certainty of the probability and zero is the impossibility of the probability.

\(0 \le P\left( E \right) \le 1\)

The probability of an event is expressed in decimals, percentages, and a fraction, and it can not be a negative value.

Types of Probability

The main three types of probabilities are:

1. Theoretical Probability
2. Experimental Probability
3. Axiomatic Probability

1. Theoretical Probability

Theoretical probability is mainly based on the possible chances of an event, that is, something to happen. Theoretical probability is based on the fact that what is expected to happen in an experiment without actually conducting it.

Theoretical probability is the ratio of the number of favourable outcomes to the total outcomes.

2. Experimental Probability

Experimental probability is a probability that is calculated based on multiple experiments. It is mainly based on the data that is obtained after an experiment is carried out.

It equals the ratio of the number of times an event occurs to the total number of times the experiments are conducted.

3. Axiomatic Probability

In axiomatic probability, a set of various rules or axioms applies to all types of events. In this type of probability, the events’ chances of occurrence and non-occurrence can be quantified based on the rules.

It equals the likelihood of an event occurring based on the occurrence of previous events.

Importance of Probability

The measurement of the possibility of an event to occur is called probability. The applications of probability in daily life are numerous. Some of the uses or importance of probability, the applications of probability in daily life plays a vital role, are discussed below:

1. Tossing a coin
2. Rolling a dice
3. Playing with cards
4. In general, example: Guessing the rain to occur today.
5. In business, to decide the probability of profit and loss
6. In medicines, to decide the possibility of the risk of disease
7. In sales, to decide the sale of the particular item
8. In selecting the objects
9. In the arrangement of objects

What are the Applications of Probability?

The measurement of the possibility of an event to occur is called probability. There are many applications associated with probability. Some of the real life applications of probability are listed below:

Application of Probability in Weather Forecast

Meteorologists collect the database related to weather and its changes worldwide by using different instruments and tools. They collect the weather information worldwide to estimate the temperature changes around the world and the weather conditions for a particular hour, day, week, month and year.

Thus, a probability forecast assesses how weather changes in terms of percentage and recording the risks associated with the weather or temperature changes to alert the people, especially in the coastal areas.

Application of Probability in Election Results

In our country, elections play a vital role in our politics. Political analysts use exit polls to measure the probability of winning or losing the candidate or parties in the elections. The probability technique is used to predict the results of voting after the election.

Application of Probability in Business

The marketing persons or salespersons promote the products to increase sales. They use the probability technique to check how much the particular product is going well in the market or not. The probability technique helps to forecast the business in future.

Application of Probability in Insurance

Insurance companies provide insurance policies or premiums based on the future forecast to the persons, vehicles etc. Insurance companies generally use theoretical probability or theory of probability to frame any particular policy and complete the policy at the premium rate. Theoretical probability is mainly based on the possible chances of an event, that is, something to happen.

Application of Probability in Medicines

The doctors give medicines to the patients to recover from the illness and build immunity power also. Doctors prefer the probability technique to check the risk factor of the patient. While giving medicines, doctors also use the concept of probability to estimate how far it is going to cure and how far it takes to recover etc.

Application of Probability in Biology

The probability technique is used in the analysis of the unnatural phenomenon.

Application of Probability in Philosophy

Philosophers use the game theory at various stages of their philosophy. Game theory is the application based on probability techniques.

Application of Probability in Game Theory

Game theory is the study of the numerical representation of strategic relations among analytical outcomes in mathematics. The key concept behind the game theory is probability techniques. It has applications in social science, system science, logical science and computer science.

Application of Probability in Games

Cricket, volleyball, soccer, football, tennis, badminton, poker, blackjack, gambling and all the board games use the concept of probability, which gives the idea about how likely a particular person or team is going to win or lose.

Application of Probability in Sports Strategies

In sports, with the help of probability, analyses are conducted to understand the strengths and weaknesses of a particular player or team. By using probability, analysts forecast the odds and outcomes regarding the team’s performance and members in the team.

By using the probability as a tool, coaches determine in which areas their team is strong enough and which areas they have to work more for the victory.

Rules of the Probability

Let \(A\) and \(B\) are two events. The five rules of probability are listed below:

Range of probability	\(0 \le P\left( A \right) \le 1\)
Addition rule of probability	\(P\left({A \cup B} \right) = P\left( A \right) + P\left( B \right) – P\left({A \cap B} \right)\)
Complimentary event	\(P\left({\underline{A} } \right) = 1 – P\left( A \right)\)
Mutually exclusive events	\(P\left({A \cap B} \right) = 0\) and \(P\left({A \cup B} \right) = P\left( A \right) + P\left( B \right)\)
Independent events	\(P\left({A \cap B} \right) = P\left( A \right) – P\left( B \right)\)
Bayes formula	\(P\left({\frac{A}{B}} \right) = P\left({\frac{B}{A}} \right) \times \frac{{P\left( A \right)}}{{P\left( B \right)}}\)

Solved Examples on Applications of Probability

Q.1. One card is drawn randomly from the well-shuffled pack of 52 cards in each of the below cases. Find the probability of getting:
(a) A queen of black colour (b) A faced card.
Ans: We know that the total number of cards in a pack is \(52.\)

(a) Number of black colour queens are \(2.\)
The probability of getting black colour queen is given by
\(P\left( E \right) = \frac{{{\text{Number}}\,{\text{of}}\,{\text{black}}\,{\text{colour}}\,{\text{queens}}}}{{{\text{Total}}\,{\text{number}}\,{\text{of}}\,{\text{cards}}}} = \frac{2}{{52}} = \frac{1}{{26}}\)
(b) Number of faced cards in the deck are \(12.\)
The probability of drawing a faced card is given by
\(P\left( E \right) = \frac{{{\text{Number}}\,{\text{of}}\,{\text{faced}}\,{\text{cards}}}}{{{\text{Total}}\,{\text{number}}\,{\text{of}}\,{\text{cards}}}} = \frac{{12}}{{52}} = \frac{3}{{13}}\)

Q.2. A bag contains 5 red balls and 7 black balls. Abhishek was selecting a ball randomly from the bag. Find the probability that a ball is drawn from the bag is black?
Ans: Given the number of red balls in a bag is \(5.\) The number of black balls in a bag is \(7.\)
The total number of balls in the bag is \(7 + 5 + 12.\)
Give, Abhishek is drawing one ball from the bag.
Probability of getting black balls
\(P\left( E \right) = \frac{{{\text{Number}}\,{\text{of}}\,{\text{black}}\,{\text{balls}}}}{{{\text{Total}}\,{\text{number}}\,{\text{of}}\,{\text{balls}}}} = \frac{7}{{12}}\)
Hence, the probability of getting a black ball from the bag by Abhishek is \(\frac{7}{{12}}.\)

Q.3. Keerthi told Mrudula to pick up a vowel from the set of English alphabets. What is the probability of taking the vowel from the set of English alphabets?
Ans: The total number of English alphabets are \(26.\)

The set of vowels In the English alphabets are \(a,e,i,o,u.\) The total number of vowels is \(5.\)
Keerthi told Mrudula to pick up a vowel.
Probability of getting a vowel \(P\left( E \right) = \frac{{{\text{Number}}\,{\text{of}}\,{\text{favourable}}\,{\text{outcomes}}}}{{{\text{Total}}\,{\text{number}}\,{\text{of}}\,{\text{outcomes}}}}\frac{5}{{26}}\)
The probability of picking a vowel from the English alphabets by Mrudula is \(\frac{5}{{26}}.\)

Q.4. Given P(E)=0.05, find the probability of ‘not E’?
Ans: Given \(P\left( E \right) = 0.05.\)
\(P\left( {\overline E } \right) + P\left( E \right) = 1.\)
Probability of not \(E = P\left( {\overline E } \right) = 1 – P\left( E \right).\)
\(P\left( {\overline E } \right) = 1 = \, – 0.05 = 0.95.\)

Q.5. The probability of two mutually exclusive events, A and B, is given by 0.5 and 0.4, respectively. Find the probability of Event A or B.
Ans: We know that the probability of events \(A\) or \(B\) is the sum of probabilities of events \(A\) and event \(B.\)
\(P\left({A \cap B} \right) = 0\) and \(P\left({A \cup B} \right) = P\left( A \right) + P\left( B \right)\)
Given, \(P\left( A \right) = 0.5,P\left( B \right) = 0.4\)
\(P(A\,{\text{or}}\,B) = 0.5 + 0.4 = 0.9\)

Summary

In this article, we have studied the definition of probability and the real life applications of probability. This article gives the formula of probability and types of probability, such as experimental, theoretical, and axiomatic probability. This article also gives the solved examples of the probability, which helps to understand the concept easily.

This article gives the uses of probability and applications of the probability in daily life in various fields like business, medicines, sports, insurance, elections and weather forecast etc.

FAQs on Applications of Probability

The following are the most frequently asked questions on applications of probability:

Q.1: What is probability?
Ans: Probability is the special branch of statistics in mathematics, which tells about a random experiment. Probability defines the possibility. 

Q.2: What is the formula of probability?
Ans: The formula of probability is the ratio of favourable events to the total number of events in an experiment.
\({\text{probability}}\left({{\text{Event}}} \right) = \frac{{{\text{Favourable}}\,{\text{outcomes}}}}{{{\text{Total}}\,{\text{number}}\,{\text{of}}\,{\text{outcomes}}}}\)

Q.3: Why is probability important in real life?
Ans: Probability defines the possibility.  In general, many events in the real life cannot be predicted with absolute certainty. For those cases, probability helps predict an event’s likelihood.

Q.4: What are the three types of probability?
Ans: The three types of probability are:
1. Theoretical Probability
2. Experimental Probability
3. Axiomatic Probability

Q.5: What are the real-life applications of probability in math?
Ans: Some of the real-life applications of probability are:
1. Rolling a dice
2. Playing a cards
3. Selling and buying
4. Sports
5. Weather forecast