Scroll to bottom of page for video examples of the unit lessons
Overview:Enduring Understandings• Probabilities are fractions derived from modeling real world experiments and simulations of chance. • Modeling real world experiments through trials and simulations are used to predict the probability of a given event. • Chance has no memory. For repeated trials of a simple experiment, the outcome of prior trials has no impact on the next. • The probability of a given event can be represented as a fraction between 0 and 1. • Probabilities are similar to percents. They are all between 0 and 1, where a probability of 0 means an outcome has 0% chance of happening and a probability of 1 means that the outcome will happen 100% of the time. A probability of 50% means an even chance of the outcome occurring. • If we add the probabilities of every outcome in a sample space, the sum should always equal 1. • The experimental probability or relative frequency of outcomes of an event can be used to estimate the exact probability of an event. • Experimental probability approaches theoretical probability when the number of trials is large. • Sometimes the outcome of one event does not affect the outcome of another event. (This is when the outcomes are called independent.) • Tree diagrams are useful for describing relatively small sample spaces and computing probabilities, as well as for visualizing why the number of outcomes can be extremely large. • Simulations can be used to collect data and estimate probabilities for real situations that are sufficiently complex that the theoretical probabilities are not obvious. |
Vocabulary
• Compound Event: Any event which consists of more than one outcome. • Empirical: A probability model based upon observed data generated by the process. Also, referred to as the experimental probability. • Event: Any possible outcome of an experiment in probability. Any collection of outcomes of an experiment. Formally, an event is any subset of the sample space. • Experimental Probability: The ratio of the number of times an outcome occurs to the total amount of trials performed. The number of times an event occurs Experimental probability = the number of times an event occurs/the total number of trials • Independent events: Two events are independent if the occurrence of one of the events gives us no information about whether or not the other event will occur; that is, the events have no influence on each other. • Probability: A measure of the likelihood of an event. It is the ratio of the number of ways a certain event can occur to the number of possible outcomes. • Probability Model: It provides a probability for each possible non-overlapping outcome for a change process so that the total probability over all such outcomes is unity. This can be either theoretical or experimental. • Relative Frequency of Outcomes: Also, Experimental Probability • Sample space: All possible outcomes of a given experiment. • Simple Event: Any event which consists of a single outcome in the sample space. A simple event can be represented by a single branch of a tree diagram. • Simulation: A technique used for answering real-world questions or making decisions in complex situations where an element of chance is involved. • Theoretical Probability: The mathematical calculation that an event will happen in theory. It is based on the structure of the processes and its outcomes. • Tree diagram: A tree-shaped diagram that illustrates sequentially the 6possible outcomes of a given event |
Unit 6: Lesson 1-4 Examples
|
|
|