Probability

Unit Review Sheet

Facts and Definitions

Lesson 1: What Is Probability?

• Probability – A measure of how likely an event is to occur.
• Probability Line – A number line from 0 to 1 used to show how likely an event is.
• Impossible (0) – Cannot happen.
• Unlikely – Not expected to happen, but still possible.
• Equal Chance (0.5) – Each outcome has the same likelihood of occurring.
• Likely – More expected to happen than not.
• Certain (1) – Guaranteed to happen.
• Sample Space – All the possible outcomes of a probability experiment (for a coin, that's {Heads, Tails}).
• Theoretical Probability – The likelihood of an event happening based on all the possible outcomes.
• Experimental Probability – The chance of something happening based on actual experiments or trials.
• Independent Event – Events where the outcome of one does not change the chance of the other.
• Favorable Outcome – The specific result you are hoping for or counting in a probability problem (e.g., landing on yellow).

Lesson 2: Observing Probability

• Prediction – A guess based on known information.
• Trial – One attempt or round of an experiment — such as a spin, roll, selection, or observation.
• Relative Frequency – How often an outcome occurs compared to the total number of trials.

Lesson 3: Probability Models

• Outcome - A possible result of a probability experiment.
• Randomness - The lack of pattern or predictability in events.
• Probability Model - A mathematical description of a random process, including all possible outcomes and their probabilities.
• Law of Large Numbers - As you increase the number of trials, the experimental probability gets closer to the theoretical probability.
• Uniform - each outcome is equally likely.
• Non-uniform - not all outcomes have the same chance of happening.
• Discrepancies between theoretical and experimental results can be caused by: Random chance (especially in small sample sizes); A biased or unfair setup (e.g., weighted die, sticky spinner); Human error in recording or conducting the experiment; and/or Incomplete or incorrect sample space.
• An organized list is a strategy that can help you organize and count outcomes when grouping events.

Lesson 4: Compound Events

• Compound Event - when two or more simple events happen together.
• Possible Outcome - a single result that could occur in an experiment or situation involving chance.
• Tree Diagram - a visual way to organize all the possible outcomes when you have two or more events.
• Compound Probability - the chance of two or more things happening together.
• Inference - using information from a sample to make a reasonable prediction about a larger group or population.
• Sample - a smaller group selected from a larger population that is used to represent the whole group.
• Population - the entire group of people or things you want to learn about or make predictions about.
• Randomly - every person or item in the group has an equal chance of being chosen.

Lesson 5: Simulations

• Replacement - Returning an item to the original set after each selection so that the conditions stay the same for every trial.
• Simulation - a way to model a real-world situation using random numbers, dice, or digital tools to predict what might happen and how often.

Lesson 6: Unit 4 Test

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Final Project: Happy Tails Dog Shelter

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