Probability theory is an essential topic for students studying mathematics at a higher level. For example, the weather forecast in some locations predicts that it will rain 50% of the time today.
The probability is the likelihood of an event occurring. The term "event" refers to one or more outcomes. The term "event" refers to a possible consequence. Total events are all possible outcomes related to the experiment posed in the question. Favorable events are sometimes known as events of interest.
This article will cover every topic in detail and at the end of the article one will be able to answer what is independent and dependent events, and their differences etc.
What is Independent and Dependent Events?
The probability or chance of an event occurring is intuitively believed to be the probability of it occurring. In the most basic circumstances, the probability of a specific event A occurring as a result of an experiment is calculated by dividing the number of ways A can occur by the total number of possible outcomes.
An independent event has no bearing on the likelihood of another event occurring (or not occurring). In other words, the occurrence has no bearing on the likelihood of a subsequent event occurring.
Independent occurrences in probability are analogous to independent events in reality. What color car you drive has nothing to do with where you work. Purchasing a lottery ticket does not affect the likelihood of having a child with blue eyes.
When two events are independent, one event does not affect the likelihood of the other.
When two events are dependent on each other, one event influences the likelihood of the other. A dependent event is dependent on another event to occur first.
Dependent events in probability are analogous to dependent occurrences in reality: If you want to go to a performance, it may be contingent on whether you receive overtime at work; if you want to see family out of the country next month, it may be contingent on whether you can obtain a passport in time.
In more technical terms, when two occurrences are dependent, the occurrence of one influences the likelihood of the other.
Example of Independent and Dependent Events:
The following are examples of independent events.
Purchasing a lottery ticket and discovering a penny on the floor (your chances of discovering a penny are not affected by purchasing a lottery ticket).
Taking a cab home and watching your favorite movie on television.
Getting a parking ticket and going to the casino to play craps.
The following are examples of dependent events.
Getting a parking citation for parking illegally. Parking illegally raises your chances of receiving a citation.
Purchasing ten lottery tickets and winning. The more tickets you purchase, the better your chances of winning.
Getting into a car accident while driving.
Differentiate Between Independent and Dependent Events:
Independent and Dependent Events Formulas:
There are more formal methods for determining whether an event is dependent or independent. These formulas can be found in basic probability.
P(A|B) = P(A).
P(B|A) = P(B)
Given that B has occurred, the chance of A is the same as the probability of A. Similarly, provided that A has occurred, the chance of B is the same as the probability of B. This is hardly surprising given that one occurrence does not affect the other.
To calculate the probability of independent events, use the following equation:
P(A∩B) = P(A) · P(B)
Events can be classified as independent or dependent in mathematics and real life. Dependent events are influenced by or affect the probability of other events, while independent events do not have any effect on each other's likelihood of occurring. When the outcome of one event determines the outcome of another, they are considered dependent, and the probability of both events occurring is the product of their individual probabilities. On the other hand, independent events occur without altering the likelihood of each other, and the probability of both events occurring is equal to the product of their individual probabilities.