Chapter 2.Conditional Probability The probabilities assigned to various events depend on what is known about the experimental situation when the assignment is made.For a particular event A,we have used P(A)to represent the probability assigned to A;we now think of P(A)as the original or unconditional probability of the event A. 2.1 The definition of conditional probability In this section,we examine how to information"an event B has occurred"affects the probability assigned to A.We will use the notation P(AB)to represent the conditional probability of A given that the event B has occurred. Conditioning is one of the fundamental tools of probability: probably the most fundamental tool.It is especially helpful for calculating the probabilities of intersections,such as P(AB). which themselves are critical for the useful Partition Theorem. Additionally,the whole field of stochastic processes is based on the idea of conditional probability.What happens next in a process depends,or is conditional,on what has happened beforehand.Chapter 2. Conditional Probability The probabilities assigned to various events depend on what is known about the experimental situation when the assignment is made. For a particular event A, we have used P(A) to represent the probability assigned to A; we now think of P(A) as the original or unconditional probability of the event A. 2.1 The definition of conditional probability In this section, we examine how to information “an event B has occurred” affects the probability assigned to A. We will use the notation P(A|B) to represent the conditional probability of A given that the event B has occurred. Conditioning is one of the fundamental tools of probability: probably the most fundamental tool. It is especially helpful for calculating the probabilities of intersections, such as P(A|B), which themselves are critical for the useful Partition Theorem. Additionally, the whole field of stochastic processes is based on the idea of conditional probability. What happens next in a process depends, or is conditional, on what has happened beforehand