Conditional probability and total probability formula are two important concepts in probability theory, and they are also common tools to solve practical problems. Conditional probability refers to the probability of another event under the condition that one event is known to occur; The total probability formula is used to calculate the total probability of an event, in which all possible situations are considered.
The calculation method of conditional probability is based on Bayesian theorem, and the formula is: P(A|B)=P(ANB)/P(B), where P(A|B) represents the probability that event A occurs when event B occurs, P(ANB) represents the probability that event A and event B occur simultaneously, and P(B) represents the probability that event B occurs.
The calculation method of the total probability formula is to decompose an event into several disjoint sub-events, then calculate the probabilities of these sub-events, and then add them to get the total probability.
The expression of total probability formula is: P(A)=∑[P(A|B_i)XP(B_i)], where B_i represents all possible sub-events of event A, P(A|B_i) represents the probability that event A will occur under the condition that B_i occurs, and P(B_i) represents B.
Conditional probability refers to the occurrence probability of event A under the condition that another event B has already occurred. Conditional probability is expressed as: P(A|B), which is read as "the probability of a under the condition of b". Conditional probability can be calculated by decision tree. The fallacy of conditional probability is to assume that P(A|B) is roughly equal to P(B|A).
Mathematician JohnAllenPaulos pointed out in his book Mathematical Blindness that doctors, lawyers and other well-educated non-statisticians often make such mistakes. This error can be avoided by describing the data with real numbers instead of probability.
Probability p (b) if event b >; 0, then the function q defined by Q(A)=P(A|B) on all events a is a probability measure. If P(B)=0, then P(A|B) is undefined. Conditional probability can be calculated by decision tree.