Find probabilities using the addition rule

Learning Objectives Define and differentiate between mutually exclusive and non-mutually exclusive events. State the General Addition Rule for the probability of the union of two events. State the Addition Rule for the probability of the union of two mutually exclusive events. Calculate P(A ∪ B) for any two events A and B. Analyze a problem to determine whether events are mutually exclusive. Solve complex word problems by applying the appropriate version of the addition rule. Interpret probabilities derived from contingency tables using the addition rule. What's more likely: drawing a King or a Spade from a deck of cards? 🃏 The answer might not be as simple as you think! This tutorial will explore the Addition Rule of Probability, a fundamental tool for calculating...

TermDefinitionExample EventA specific outcome or a set of outcomes from a random experiment.When rolling a standard six-sided die, 'rolling an even number' is an event that includes the outcomes {2, 4, 6}. Sample Space (S)The set of all possible outcomes of a random experiment.The sample space for rolling a standard six-sided die is S = {1, 2, 3, 4, 5, 6}. Union of Events (A ∪ B)The event that either event A or event B (or both) occurs. The key word is 'OR'.If A is 'rolling an even number' {2, 4, 6} and B is 'rolling a number less than 4' {1, 2, 3}, then A ∪ B is {1, 2, 3, 4, 6}. Intersection of Events (A ∩ B)The event that both event A and event B occur simultaneously. The key word is 'AND'.Using the events from the previous example, A ∩...

General Addition Rule P(A \cup B) = P(A) + P(B) - P(A \cap B) Use this rule to find the probability of event A or event B occurring. It works for ALL situations, including both mutually exclusive and non-mutually exclusive events. The final term, P(A ∩ B), corrects for double-counting the outcomes that are in both A and B. Addition Rule for Mutually Exclusive Events P(A \cup B) = P(A) + P(B) This is a simplified version of the general rule used only when events A and B are mutually exclusive. Since they cannot happen at the same time, their intersection is zero (P(A ∩ B) = 0), so the subtraction term is unnecessary.