# Conditional Probability

Based on a previous event or outcome, the conditionality probability is characterized as the probability of an event or product. Conditional probability shall be compared with the modified chance of the successor or dependent circumstance by multiplying the previous event's possibility.

● Event A is to admit an individual applying for a university. This person is likely to be admitted to college by 80 percent.

● Event B is that this individual is provided dormitory quarters. Just 60 percent of all approved students will be provided with dormitory housing.

● P = P = Dormitory Housing (accepted) P = (0.60)*(0.80) = 0.48. P = (accepted) = 0.48.

These two cases - the likelihood of you being admitted to college and being equipped with dormitories, would be seen as a conditional probability.

The likelihood can be compared with the probability without conditions. Unconditional probability refers to the likelihood of an occurrence happening, regardless of the existence of any other event or circumstances.

The likelihood of one occurrence with any relationship to one or more other events is a prerequisite. Examples include:

Event A is that it rains outside, and today it can precipitate 0.3 (30 percent).

Event B is where you have to go out, and it has a 0.5 chance (50 percent).

A conditional distribution will glance at these two phenomena in conjunction with each other - a chance of both raining and going out.

The formula for Conditional Probability:

P (B|A) = P (A∩B) / P (A)

● A cold front is moving into your country.

● Precipitation the formation of clouds,

● A different show that drives away the rain clouds.

Then we conclude that the conditional likelihood of rainfall depends on all the events described above.

**Conditional Probability vs. Joint Probability and Marginal Probability**

The conditional probability says that p (A|B) occurs the chance that event A happens as event B. Example: when you drew a red card, what is the likelihood of it being a 4 (p(four|red))=2/26=1/13. So there are two fours out of 26 red cards (which have a red card).

Marginal probability: the possibility that an occurrence (p(A)) occurs can be considered an unconditional probability. It's not subject to a different case. Example: The chances of a card being drawn are red (p(red) = 0.5). Another instance: a 4 (p(four)=1/13) card drawing is probable.

Joint likelihood: p (A and B). The probability of event A and event B. It is the likelihood that two or more events will collide. The possibility of the cross-references of A and B is p (A to B). Example: the chances of a four-card and red = p(four and red) = 2/52=1/26. (Adequate deck with 52, 4 hearts and four diamonds have two red fours).

**Bayes' Theorem**

Bayes' theorem is a mathematical formula to evaluate conditional probability, named after British mathematician Thomas Bayes from the 18th century. The theorem offers a way to amend current (update probability) predictions and hypotheses based on new or additional proof. In finance, Bayes' theorem can be used to assess the likelihood that potential borrowers will be lent money.

The theorem of Bayes is also known as the "Rule" of the Bayes and is the base of statistics in the Bayesian language. This set of probability rules helps you update your forecasts of events based on new knowledge and better and dynamic assessments.