In probability theory, the chain rule[1] (also called the general product rule[2][3]) describes how to calculate the probability of the intersection of, not necessarily independent, events or the joint …

Even though the visual example (with equally likely outcome spaces) is useful for gaining intuition, condi-tional probability applies regardless of whether the sample space has equally likely outcomes! …

If $C$ is the event that it is cloudy, then we write this as $P (R | C)$, the conditional probability of $R$ given that $C$ has occurred. It is reasonable to assume that in this example, $P (R | C)$ should be …

Aug 6, 2021 · We move $P (A_1)$ term to the LHS and apply definition of conditional probability to get the new LHS. And also rearrange the $A_1$ sub-term to the very end of the conditional probability …

Jul 11, 2025 · In fact, we can say that $A$ has occurred if and only if $A \cap B$ has occurred. So, if we know that $B$ has occurred, the conditional probability of $A$ given $B$ is $\map \Pr {A \cap B}$. It …

Detailed tutorial on Bayes’ rules, Conditional probability, Chain rule to improve your understanding of Machine Learning. Also try practice problems to test & improve your skill level.

The chain rule is used when you have multiple trials, meaning that you want to measure several events one after another. In these cases you need to multiply the probability of the first event by the …

Conditional Probability, equally likely outcomes. The conditional probabilityof "given ’is the probability that "occurs given that F has already occurred. This is known as conditioning on F. With equally likely …

We can also define the probability of an event conditional upon "evidence" of another event. Let's consider the following Venn diagram to illustrate this concept:

The chain rule allows us to compute a probability that the forward sampling function takes a given path. The chain rule seems innocent but is used heavily in Bayesian statistics.