What is conditional probability?

Conditional probability is the probability of an event occurring given that another event has already occurred.

Conditional probability is a measure of the likelihood of an event occurring, given that another event has already occurred. It is denoted by P(A|B), where A and B are events. The vertical bar '|' means 'given that'. For example, P(A|B) means the probability of event A occurring given that event B has already occurred.

The formula for conditional probability is:

P(A|B) = P(A and B) / P(B)

where P(A and B) is the probability of both events A and B occurring, and P(B) is the probability of event B occurring.

Conditional probability can be used in a variety of real-world situations, such as medical diagnoses, weather forecasting, and financial analysis. For example, in medical diagnoses, the probability of a patient having a certain disease may depend on their age, gender, and other factors. By using conditional probability, doctors can make more accurate diagnoses and provide better treatment.

It is important to note that conditional probability is not always the same as the unconditional probability of an event. For example, the probability of rolling a 6 on a fair die is 1/6. However, if we know that the die has already rolled an odd number, the probability of rolling a 6 is now 0, since it is impossible to roll a 6 on an odd number.