Dependent Events

An event can be an everyday situation like a student doing well in exams or a player winning the match for his team. Now imagine if the student scored well in his exam and that affected his performance during the football match allowing him to score. You will notice that the first event affected the outcome of the second event, so we say it is dependent on each other. Dependent events are usually real-life events, and if there are two events, the outcome of the first event will change the outcome of the second event.

We know that the probability is: Probability = Favorable Outcome/Possible Outcome 

Based on this to know the probability of both events happening we use the formula:

P( A and B) = P(A) × P(B | A)

Where: 
P(A) is the probability of the first event occurring.
P(B | A) is the probability of the second event occurring after the first event has already occurred.

The main thing to know is that the probability of the second event occurring depends on the outcome of the first event.

In probability, we often classify events into two categories: independent events and dependent events

The difference between the two events is given below:
 

There are many properties of dependent events that we need to know. Some of the main properties are mentioned below:

• The outcome of an event is affected by the outcome of a previously occurred event.

• The probability is changed after each event. So once an event happens the possible outcomes change for the next event.

• Dependent events are not always directly dependent on each other. For e.g., the weather can affect the number of road accidents on a particular day. Here, weather and the number of accidents are not always dependent on each other.

Dependent events are important because they tell us the relationship between two events and how they affect each other. Here are some reasons why dependent events are important:

• Dependent events help in making decisions. This is because when one event influences another event it can benefit businesses on future planning and strategies.

• When events are dependent on one another, it allows us to make accurate predictions. This helps when we want to predict the weather change or a market trend.

• In service industries like healthcare, understanding the dependency of events helps in better resource allocation. For example, if a patient is being treated and needs a diagnosis it would affect the resources needed for the next stage of care.

Dependent events are quite easy to learn, but students can get confused. So here are a few tips and tricks to master dependent events:

• Memorize the formula of dependent events: P(A and B) = P(A) × P(B | A). It is important to memorize the formula and understand the key terms. Here, P(A) indicates the probability of the occurrence of the first event, and P(B | A) is the probability of the second event occurring after the first event.

• Adjust the sample space after the first event: As soon as the first event happens, the number of total outcomes automatically decreases. This means that the probability of the next event is based on the remaining items. 

• Practice with real-life situations: Take real-life situations and try to find whether any event is dependent on each other. This can give us a better understanding of how dependent events works.

We use the concept of dependent events on a daily basis. It is widely used in environmental sciences and various other fields.

• To accurately predict the weather: Meteorologists use dependent events to accurately predict the weather conditions and to find the probability that the weather tomorrow depends on today's weather conditions. 

• Sports strategies: Sports analysts use dependent events to predict whether the team is going to win or lose based on their previous performance and their score in the current game.

• Education: Educational institutes use dependent events to determine whether a student is going to pass based on the students’ previous performance in earlier exams.