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What are Mutually Exclusive Events? | Probability Theory, Disjoint Events

What are mutually exclusive events? Events that are mutually exclusive are events that cannot both occur simultaneously. For example, flipping tails and flipping heads are mutually exclusive events! We cannot flip both talks and heads in one flip of a single coin. More formally, two events are mutually exclusive if their intersection is empty. Another word to describe this is "disjoint", two events are mutually exclusive if they are disjoint. That means they have no common elements! If A and B are mutually exclusive events then there is no possible outcome that is in both A and B! What does this mean regarding probability? Well, if A and B are mutually exclusive events, then P(A U B) = P(A) + P(B), which is a special case of what's called the addition rule of probability. Also, P(A intersect B) = 0, which is a special case of the multiplication rule of probability. These should both seem fairly intuitive. Since A and B have no intersection, we can add up their probabilities to get the probability of their union, and in doing so we aren't double counting anything. Also, since they have no intersection, the probability of A intersect B is clearly 0, since they cannot both occur. If you are preparing for Probability Theory or in the midst of learning Probability Theory, you might be interested in the textbook I used in my Probability Theory course, called "A First Course in Probability Theory" by Sheldon Ross. Check out the book and see if it suits your needs! You can purchase the textbook using the affiliate link below which costs you nothing extra and helps support Wrath of Math! PURCHASE THE BOOK: https://amzn.to/31mXEjr I hope you find this video helpful, and be sure to ask any questions down in the comments! +WRATH OF MATH+ ◆ Support Wrath of Math on Patreon:   / wrathofmathlessons   Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● Facebook:   / wrathofmath   ● Twitter:   / wrathofmathedu   My Music Channel:    / seanemusic