- [[joint probability of dependent events]] # Idea Joint probability is denoted as $P(A \ \text{and} \ B)$ or $P(A \cap B)$ or $P(A, B)$ (read "the probability of A and B jointly occurring"). It's also known as the intersection of $A$ and $B$. The joint probability of **independent** events (i.e., events that don't influence each other) is the product of the individual probability of each event occurring (known as the **[[multiplication rule]]**). $P(A,B) = P(A) P(B)$ ![[20230821122346.png]] The probability of flipping a fair coin and obtaining *head* **and** flipping another unfair coin (30% probability getting tail) and obtaining *tail*: $P(head, tail) = 0.5 * 0.3 = 0.15$ Possible outcomes: head-head, head-tail, tail-head, tail-tail ![[s20220325_211327.png]] If we flip a fair coin three times, the probability of obtaining 3 heads is $0.5 * 0.5 * 0.5$ (multiplication rule). Each flip is **independent** of one another. That is, the outcome of each flip doesn't influence the other flips' outcomes. # References - [Joint Probability Definition](https://www.investopedia.com/terms/j/jointprobability.asp)