Probability is a branch of mathematics to find the numerical deductions from the occurrence of a random event in a known environment. When we say “known”, we mean that the environment where we are experimenting follows the general rules of truth. For example: When a coin is tossed and the probability of heads showing up is to be determined then it is assumed that the fact “Coin has only two sides with one being head and another being tail” is well established.
Probability is calculated to predict the outcome of an event where event results can be predicted with certainty. The likeliness of an outcome can be calculated via probability. The detailed analysis of results obtained can be processed further by applying statistical models to derive insightful information.
Many times, the outcomes of events are uncertain. In probability, we try to measure the chances of the occurrence of such outcomes. Backed with knowledge and data gathering, it is possible to calculate the probable number of outcomes. Thus, it is necessary to have in-depth knowledge on data tips and tricks and use it to find probability in statistics.
What Are The Applications Of Probability? Where Is It Used?
Probability is a powerful method to predict the outcomes. How often have you come across some of these questions like:
- 100 people are participating in the voting process, what are the chances of Democrats winning the elections?
- What is the probability of me winning the lottery?
- What is the probability of 1 showing up when a dice is rolled?
- What are the chances of three heads showing up simultaneously when three coins are flipped together?
These questions can be answered by probability provided all linked data. These outcomes can be used as a parameter to decide on the next course of action.
Some major applications of probability can be seen in the form of :
- Weather Forecasting: Predicting weather forecasts is one of the major applications of probability in statistics. If you are planning for a trip to the hill station, this application becomes very useful to get the weather prediction for that period.
- Stock Exchange Market: Stockbrokers use probability coupled with many other factors like current market situations, investments, the profit of the previous quarter and more to find the suitable stocks for investment. There are a lot of activities in the stock market that depend very much on probability and statistics.
- Insurance Industry: Insurance industry is operated on the grounds of probability. The premium amount very much depends upon the insurer’s age, medical history, family income, genetic disorders and a lot more. A huge chunk of information for the insurer is obtained to run the statistical and probability models to maximise the profit margins.
- Sports Strategy: You might have seen batting average in cricket, the average number of goals by a player in football, the probability and statistics are used to determine the suited player to be sent next during a match.
- Lottery Market: Lottery market is the whole pursuit of possibilities. People play on probable chances and calculations using probability techniques to win. You might have seen that sometimes one player buys most of the lottery tickets to improve the winning chances or one player buys tickets from different shops, again and again, all of these are the part of strategies used to improve odds of winning owned by the laws of probability.
How To Calculate Probability?
Probability is calculated between 0 and 1 with 0 being the impossible chances of occurrence and 1 being the surety of occurrence. To find the probability of any event two parameters are required:
- Number of all possible outcomes
- The number of favourable outcomes.
Probability = Number of favourable outcomes / Number of all possible outcomes
Example 1: What is the probability of getting 1 when an unbiased dice is rolled.
Solution with explanation:
Number of all possible outcomes: 6
Number of favourable outcomes: 1
Here, the keyword is unbiased dice. This experiment assumes that the dice is a standard dice used for playing having 1 to 6 numbers engraved. To calculate probability all the relevant data should be provided.
Example 2: What is the probability of getting Head when a biased coin is flipped with both the sides being head?
Solution with explanation:
Number of all possible outcomes: 1
Number of favourable outcomes: 1
Here, the keyword is a biased coin. Since the coin has heads on both the sides then the chances of heads showing up are certain. Here the results of the experiment are different because the environment where the experiment is being conducted is changed.
Note: Probability of event A occurring: P(A)
Probability of event B occurring: P(B)
- If P(A) > P(B), then the chances of event A occurring is more than B.
- If P(B) > P(A), then the chances of event B occurring is more than A.
- If P(A) = P(B), then the chances of event A occurring is equal to B.
How many types of probability are there?
Probability can be categorised into these :
- Theoretical Probability: This type is based on the favourable and the total number of events obtained after experimenting on a theoretical basis. Other extremities are avoided while calculating probability theoretically. For example, when a coin is flipped then the theoretical probability of heads showing up is ½. Here what if the coin gets missed during flipping or probability results could not be obtained due to any external reason? These extremities are eliminated and ideal conditions are assumed.
- Relative Probability: In this type, an experiment is conducted multiple times and the frequency of occurrence is used to calculate the probability. For example: If we are trying to track down the relative probability of an event A occurring then it can be calculated as:
The probability of event A: How many times an event A occurs / How many trials of an experiment conducted.
- Conditional Probability: Conditional probability of an event occurrence is calculated based on the occurrence of the previous event. For example: What is the probability of me getting wet in the rain today? It has two likeliness of two events occurring, one is the probability of today being a rainy day and other is me going out today.
- Subjective Probability: In this type, the value of probability (between 0 and 1) is based out of personal opinion. It is assigned by individuals based on their evaluation of the likelihood of event occurrence. For example, The probability of me being asked out of lunch is 0.1.
Event is associated with an action. For example: Flipping a coin to get “Heads” is an event or rolling dice with “1” being obtained is an event.
These events can be of different types like:
- Independent Events: These types of events are not affected by the occurrence of other events. As the coin is flipped it would not know what was the outcome of the previous flipping event. Every time a new coin flipping is an isolated event. Nothing is taken into consideration from previous events when a series of independent events are considered for probability calculations.
- Dependent Events: These types of events are affected by the outcomes of previous events. It is used more in the real world like when a stock market-related predictions are made then all the possible previous events are considered to reach the accurate prediction. There can be one or more events in the past that may impact the current results. For example: What is the probability of drawing a king on the 3rd card? Here, the probability changes after every draw. Till the 3rd card is reached maybe kind has already been drawn in any of the previous draws or not. All of these past events are to be considered to reach accurate predictions in case of dependent events.
- Mutually Exclusive Events: Such events cannot go together. In case two events can never occur at the same time then they are termed as mutually exclusive events. For example, one person cannot tell a lie or truth at the same time or a coin cannot get heads and tails at the same time when the coin is flipped once.
There are a lot of topics in probability that are not covered in this article but we have tried to cover the basics of probability in statistics to get you started. The more you dig deeper into probability, the more interesting it gets. One of the buzzwords nowadays “Data science” uses probability and statistics to mine insights out of terabytes of data generated every day. Probability is undoubtedly a shining star in the universe of mathematics lending its shine to various linked sciences.
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