Joint probability distribution using conditional probability

We can use the product rule to formulate conditional probability in the form:

$$P(a\wedge b)=P(a|b)P(b)=P(b|a)P(a)$$

A general version holds for joint distributions:

$$P(\text{Weather},\text{Cavity})=P(\text{Weather}|\text{Cavity})\cdot P(\text{Cavity})$$

(we interpret this as $4\cdot 2=8$ set of equations, not using matrix math)