Joint Probability

Joint probability is the likelihood of multiple events all occurring.

The joint probability $P(x,y)$ is the probability of both $x$ and $y$ happening.

• Sometimes also denoted $P(x\cap y)$

$P(x\cap y)=P(x|y)P(y)$

P(x \cap y) \neq P(x) P(y)

The above is only true is $x$ and $y$ are independent, in which case $P(x|y)=P(x)$. Also, keep thinking in my head that $P(x|y)P(y)=P(x)$, which is simply not true (it’s true for )

Related

• Conditional Probability