Conditional probability is a measure of the likelihood of an event occurring given that another event has already occurred. It is calculated by dividing the probability of the joint occurrence of both events by the probability of the first event.
Regular probability considers the likelihood of an event occurring without any prior knowledge or conditions, while conditional probability takes into account the occurrence of another event before calculating the likelihood of the desired event.
One common example of conditional probability is in medical testing. The probability of a person having a disease given a positive test result is an example of conditional probability. Another example is the probability of getting into a car accident given that it is raining outside.
Conditional probability is calculated by dividing the probability of the joint occurrence of two events by the probability of the first event. This can be written as P(A|B) = P(A∩B) / P(B), where A and B are events.
If two events are independent, then the conditional probability of one event occurring given the other event has occurred is equal to the regular probability of the first event. In other words, the occurrence of one event does not affect the likelihood of the other event occurring, and the conditional probability is the same as the regular probability.