Probability of opposite, mutually exclusive, and overlapping events

Learning Objectives Define and identify opposite (complementary) events. Calculate the probability of an opposite event occurring. Distinguish between mutually exclusive and overlapping events. Apply the correct formula to calculate the probability of mutually exclusive events. Apply the correct formula to calculate the probability of overlapping events. Solve real-world problems involving opposite, mutually exclusive, and overlapping probabilities. Have you ever wondered about the chances of something *not* happening, or the likelihood of one thing *or* another occurring? 🤔 Probability helps us understand these possibilities! In this lesson, we'll explore different types of events and how to calculate their probabilities. You'll learn about events that can'...

TermDefinitionExample ProbabilityThe measure of how likely an event is to occur, expressed as a number between 0 and 1 (or 0% and 100%).The probability of flipping a coin and getting heads is 1/2 or 50%. EventA specific outcome or a set of outcomes from an experiment or situation.Rolling a '4' on a standard six-sided die is an event. Opposite Event (Complement)The event that an original event does *not* occur. If 'A' is an event, its opposite is denoted as A' (read as 'A prime' or 'not A').If event A is 'rolling an even number', then A' (the opposite event) is 'rolling an odd number'. Mutually Exclusive EventsTwo events that cannot happen at the same time. If one event occurs, the other cannot.When rolling a single die,...

Probability of an Opposite Event $P(A') = 1 - P(A)$ To find the probability that an event A does *not* happen, subtract the probability of A happening from 1 (or 100%). This is useful when it's easier to calculate the probability of the event happening than not happening. Probability of Mutually Exclusive Events (OR Rule) $P(A \text{ or } B) = P(A) + P(B)$ If two events, A and B, cannot occur at the same time (they are mutually exclusive), the probability that either A *or* B occurs is the sum of their individual probabilities. Probability of Overlapping Events (OR Rule) $P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$ If two events, A and B, *can* occur at the same time (they are overlapping), the probability that either A *or* B occurs is the sum...