Conditional probability is a mathematical concept that measures the likelihood of an event occurring given that another event has already occurred. It is represented as P(A|B), where A is the event we are interested in and B is the event that has already occurred.
Conditional probability is calculated by dividing the probability of the joint occurrence of events A and B by the probability of event B. In other words, P(A|B) = P(A and B) / P(B).
The main difference between conditional probability and regular probability is that regular probability measures the likelihood of an event occurring without any other information, while conditional probability takes into account the occurrence of another event.
One example of a conditional probability question is: If a deck of cards contains 52 cards, including 26 red cards and 26 black cards, what is the probability of drawing a red card given that the first card drawn was a black card? This can be represented as P(Red|Black) = 26/51.
Conditional probability is used in various fields such as statistics, economics, and biology to make predictions and decisions based on the occurrence of certain events. For example, in medicine, conditional probability can be used to determine the likelihood of a patient having a certain disease based on their symptoms and medical history.