Certain, probable, unlikely, and impossible

Learning Objectives Define and differentiate between certain, probable, unlikely, and impossible events. Classify given events as certain, probable, unlikely, or impossible. Place events on a probability scale ranging from impossible to certain. Compare the likelihood of different events using appropriate terminology. Provide real-world examples for each category of event. Explain why understanding likelihood is important in daily life. Have you ever wondered if it will rain tomorrow? 🌧️ Or if you'll win a game of chance? How sure are you about these things? In this lesson, we'll explore how to describe the likelihood of events happening, using terms like certain, probable, unlikely, and impossible. Understanding these concepts helps us make better predictions and...

TermDefinitionExample Certain EventAn event that will definitely happen; its probability is 1 (or 100%).The sun will rise tomorrow. Impossible EventAn event that will never happen; its probability is 0 (or 0%).A human jumping to the moon without any equipment. Probable Event (Likely Event)An event that is likely to happen, but not guaranteed; its probability is greater than 0.5 but less than 1.It will be sunny in July where you live (assuming a summer month). Unlikely EventAn event that is not likely to happen, but is still possible; its probability is greater than 0 but less than 0.5.Winning the grand prize in a national lottery. Equally Likely EventEvents that have the same chance of happening; for two outcomes, each has a probability of 0.5.Flipping a fair coin and getting heads or tai...

The Probability Scale Range $0 \le P(\text{event}) \le 1$ The probability of any event happening is always a number between 0 and 1, inclusive. A probability of 0 means the event is impossible, and a probability of 1 means the event is certain. Mapping Likelihood Terms to the Scale $ \begin{cases} P(\text{event}) = 0 & \text{Impossible}\\ 0 < P(\text{event}) < 0.5 & \text{Unlikely}\\ P(\text{event}) = 0.5 & \text{Equally Likely}\\ 0.5 < P(\text{event}) < 1 & \text{Probable (Likely)}\\ P(\text{event}) = 1 & \text{Certain} \end{cases} $ This rule connects the descriptive terms of likelihood to specific numerical probability values or ranges on the probability scale, providing a quantitative understanding of each term. Comparing Likelihood of...