# Understanding Conditional Probability and Probability Formulas

Comprehensive Definition, Description, Examples & RulesÂ

## Introduction to Probability

Probability or P/A or P/B is a statistical concept. The occurrence of random events is dealt by probability concepts. Probability is the possibility of the outcome of any event. It is helpful in making predictions and decisions. You will learn about its meaning, significance, and formula on this page. In the end, there is a worksheet to check the practical understanding of the probability concept among students.

### Probability and its significance in statistics.

Probability is the possibility of the outcome of any event. The value of probability can be observed from one to zero. This concept is useful inÂ

- Making predictions.
- You can make decisions through the probability concept. It is used in fields like the stock market and so on.
- This concept is also useful in fields like medicine etc.

### How is probability used in making decisions?

You can make decisions in your daily life through this concept:Â

- You can predict the weather by using the probability concept.
- You can purchase shares and stocks by making predictions.
- In the medical sector, it is useful in making decisions for treatment on the basis of symptoms.

## Conditional Probability Fundamentals:

### Conditional probability and its significance.

Â It is used for calculating the probability of A on the basis of B. Conditional probability is significant in the real world. This concept is useful in making decisions, and it is also relevant in fields like science, physics, and so on.

### The concept of events in conditional probability.

There are two events in conditional probability, which are denoted as events ‘A’ and ‘B’.

- In this, you have to calculate the event ‘A’ probability on the basis of ‘B’ information.
- Event ‘A’ dependence on event B.

## Conditional Probability Formula

Conditional probability is a probability theory in which one event depends on the information of another event.

### Conditional probability formula: P(A|B) = P(A âˆ© B) / P(B).

The conditional probability formula is

P(A|B) = P(A âˆ© B) / P(B).

- In this formula, P(A|B) is the probability of events A and B.
- P(A âˆ© B) is the probability of both events altogether.
- P(B) is the probability of the occurrence of event B.

## Probability Formula Overview:

There are various probability formulas that we use in probability. You will learn about the conditions of each formula in this section.

### Marginal Probability: P(A):

It is the single event probability, like the occurrence of event ‘A’ without depending on other events.

The formula for margin probability is:

- Favorable outcome/total number of outcomes

### Joint Probability: P(A âˆ© B):

It is the probability of two events occurring together. The formula for joint probability is:

- Favorable outcome for (A and B) or total outcomes

### Conditional Probability: P(A|B):

Conditional probability is a probability theory in which one event depends on the information of another event. The conditional probability formula is:

- P(A|B) = P(A âˆ© B) / P(B)

### How these formulas are interconnected.

- P(A): It deals with the probability of a single event.
- P(A âˆ© B): It deals with the probability of events A and B together.
- P(A|B): It deals with the probability of event A by considering the information from event B.

### Probability of A Given B :

The meaning of probability a given bÂ P(A|B) is the dependence of event A and event B. It deals with the probability of event A by considering the information from event B.

**Examples to illustrate the concept.**

You can develop an understanding of this concept with the help of these examples:

- You need to find out the probability of getting a tail on a coin.
- The probability to get a tail on the first coin is Â½ or get a tail on the second coin is Â½ because there are two outcomes, head or tail.

By using this formula, you can get the answer P(A|B) = P(A âˆ© B) / P(B).

Â¼ / Â½ = Â¼ / Â½ = Â½

## Conditional Probability Equation

- The first step includes Identification of the events that you can refer to as Event A and Event B.
- You need to determine the probability of event A, i.e., P(A), and then the probability of event B. The probability you will find is P(Aâˆ©B).
- You need to apply the conditional probability formula to calculate conditional probability.

For example

In a deck of 52 cards where two cards are being drawn, the event would be:

- A: drawing a black card on the first draw and
- B: Draw a black card on the second draw.

The conditional probability of drawing a black card on the second draw (B), given that we drew a black card on the first draw (A), is P(B|A).

After drawing a black card on the first draw, there are 25 black cards and 51 cards remaining in the deck. So, P(B|A) = 25/51 = 0.49 (approximately 49%).

### Probability of B Given A:

In this condition, you need to find the probability of event B on the basis of event A information.

It deals with the probability of event B by considering the information from event A. It is helpful in finding the probability under the conditions where event A is known.

### Compare and contrast “P(A|B)” and “P(B|A).”

- P(A|B) is the probability of event A on the basis of event B information, and P(B|A) is the probability of event B on the basis of event A information.
- P(A|B) is used for making predictions in comparison to P(B|A).

## Conditional Probability vs Bayes Theorem:

They are both related to each other, but the concepts are different in probability. Conditional probability is a probability theory in which one event depends on the information of another event.

### The contrast between conditional probability vs Bayes theorem

When one event gets done, we refer to it as conditional probability P/A.

The conditional probability formula is P(A|B) = P(A âˆ© B) / P(B).

You can make decisions with the help of this conceptÂ

In its comparison, the Bayes theorem is calculated on the basis of prior probabilities. Its formula is P(B) A. The P(A)/P(B) Bayes theorem is useful in digital concepts.

### Examples of situations where each is more applicable.

- You can find out the probability of passing students in all the subjects using conditional probability.
- In Bayes’s theorem, you can use this concept with medical diagnosis and digital concepts.

## Applications of Conditional Probability:

Conditional probability can be used in daily life. It is also relevant in various sectors, including healthcare and so on.

### Practical applications of conditional probabilityÂ

- Medicine: In the medical field, conditional probability is used for calculating the probability of treatment and diagnosis methods. It is also used in determining the genetic disorder in the child at the time of birth.
- Finance: In finance, conditional probability is used to calculate the probability of the stock market or shares.
- Weather forecasting: It is also relevant in forecasting good weather. You can find out the raining probability with conditional probability.

Whether the concept of conditional formatting is used in medicine or any other sector, It becomes useful in making the right decision. You can easily predict something and come to a conclusion by using the concept of probability.

## Visualizing Probability:

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## Key Takeaways

- Probability is the possibility of the outcome of any event. The value of probability can be observed from one to zero.
- This concept is useful in making decisions, and it is also relevant in fields like science, physics, and so on.
- Conditional probability is a probability theory in which one event depends on the information of another event.
- You can improve your probability concept by practicing on the worksheet given on this page.

## Quiz

#### Question comes here

## Frequently Asked Questions

It is a probability theory in which one event depends on the information of another event. The conditional probability formula is P(A|B) = P(A âˆ© B) / P(B).

Conditional formatting is useful in the medical field for predicting weather and so on.

The common probability formulas are as follows: P(A): It deals with the probability of a single event. P(A âˆ© B): It deals with the probability of events A and B together. P(A|B): It deals with the probability of event A by considering the information from event B.

It becomes useful in making the right decision. You can easily predict something and come to a conclusion by using the concept of probability.

Conditional probability is used to find out the probability of event A on the basis of event B information. The Bayes theorem is used for calculating the probability of a prior event on the basis of a new event.

You can calculate the conditional probabilities for more than two events using the Bayes theorem.