Final answer:
Probability theory involves joint probability, simple (or marginal) probability, and techniques for visualizing and computing these probabilities, such as using contingency tables, Venn diagrams, and tree diagrams, along with applying the multiplication and addition rules of probability.
Step-by-step explanation:
The concepts related to probability theory include joint probability, which is the probability of two events happening together; simple (or marginal) probability, which is the probability of just a single event occurring; and the ability to perform visualizing and computing probabilities using diagrams and calculations.
The multiplication rule—P(A AND B) = P(A|B)P(B)—is used to calculate the probability of both A and B occurring, which is relevant for joint probability. Meanwhile, the addition rule—P(A OR B) = P(A) + P(B) − P(A AND B)—is employed when one needs to compute the likelihood of either event A or B or both occurring, relevant to understanding combined or total probability involving multiple events.
Understanding these fundamental rules is crucial to determining if events are independent or dependent and if they are mutually exclusive or not. Various visual aids like contingency tables, Venn diagrams, and tree diagrams are also instrumental in calculating and visualizing these probabilities.