The probability of A conditioned on B, denoted P (A|B), is equal to P (AB)/P (B). The division provides that the probabilities of all outcomes within B will sum to 1. Conditioning restricts the sample space to those outcomes which are in the set being conditioned on (in this case B).

p（ab）表示事件a和b同时发生的概率，若ab事件分步发生则p（ab）=p（a）p（b|a）或者p（b）p（a|b）；也可通过p（ab）=（a交b中的样本点数）/（样本空间中总的样本点数），这要看题目是否方便模型的建立。 ps：才开始学概率论的条件概率，如有错误，那就错了。

$$P(A)=P(A\Omega)=P(A\cap (B\cup B'))=P((A\cap B)\cup (A\cap B'))=P(AB)+P(AB'). $$ Where the last equality stands because AB and AB' have no intersections.

Mar 16, 2019 · $\begingroup$ $P(A|B)$ is the probability of $A$ occurring given that $B$ has already occurred while $P(AB)=P(A\cap B)$ is the probability of $A$ and $B$ both occurring together without any premise of either of them being already occurred.

P(A/B) formula is given as, P(A/B) = P(A∩B) / P(B), where, P(A) is the probability of the event A, P(B) is the probability of the event B, and P(A∩B) is the probability of happening of both A and B.

Jan 5, 2021 · P(A and B) – Written form; P(A∩B) – Notation form; The way we calculate this probability depends on whether or not events A and B are independent or dependent. If A and B are independent, then the formula we use to calculate P(A∩B) is simply: Independent Events: P(A∩B) = P(A) * P(B)

Formula for the probability of A and B (independent events): p(A and B) = p(A) * p(B). If the probability of one event doesn’t affect the other, you have an independent event. All you do is multiply the probability of one by the probability of another.

$p(a|b)$ = the probability of event a happens given that the event b happens. The difference in words is critical. None of these have the sense of causation that due to implies. If b is unlikely, but a happens all the time b does, $p(a|b)$ can be quite high.

P(B|A) means "Event B given Event A" In other words, event A has already happened, now what is the chance of event B? P(B|A) is also called the "Conditional Probability" of B given A.

In this article, we learn the definition of conditional probability P (A|B), formula, and solved examples on conditional probability. Bayes’ theorem describes the probability of occurrence of an event related to any condition. This theorem is considered for the case of conditional probability.