P - Probability Module Overview
Probability Module Overview
Introduction
In this unit, students will learn to determine likelihood of an event, calculate theoretical and experimental probabilities, and compare the experimental to the experimental calculations. Students will learn to work with ratios to represent the theoretical probabilities and find and create representations for sample spaces for both simple and compound events. Using data to make predictions and experiments to check those predictions will be part of this unit. Students will also learn to set up and use simulations to generate frequencies and predict outcomes in events.
Then students will use measures of center and variability to help describe different populations and make comparisons between two populations. Students will learn how to complete a random survey showing a more accurate reflection of the population being surveyed. Students will use random sampling data to analyze a population.
Essential Questions
- How can you describe the likelihood of an event?
- How can you find the experimental probability of an event?
- How can you find the theoretical probability of an event?
- How do you set up a simulation?
- How can simulations be used for estimating probabilities?
- How can you make decisions based on predictions?
- How can you create a probability model?
- How do you find the probability of compound events represented by tables, tree diagrams, and simulation?
- How can you use measures of center and variability to compare two populations?
- How can you use a sample to gather information about a population?
- How can samples be used to make predictions about a population?
- Why is a random sample more reflective of the population than other means of sampling?
Key Terms
The following key terms will help you understand the content in this module.
Box Plot-Also known as the box and whisker plot is a way to show the distribution of data based on the five number summary-minimum, first quartile, median, third quartile, and maximum.
Complement- the set of all outcomes that are not in the event
Dot Plot-Statistical chart made up of data points on a number line.
Event- the outcome of an experiment or situation
Experiment- an activity involving chance
Experimental Probability-the ratio of the total number of times the favorable outcome occurs to the total number of trials, or times the experiment is performed.
Fundamental Counting Principle- a method used to find the number of possible outcomes by multiplying the number of possible outcomes of each separate event
Long-Run Relative Frequency- The long-run relative frequency is the number that the relative frequencies get closer and closer to as more and more trials are performed.
Measures of Central Tendency- The typical value or central position in a data set. Mean, median and mode can be used to describe this point.
Measures of Variability or Spread-How varied or spread out your data is. Range, mean absolute deviation, and interquartile range can describe the variability.
Outcome- each result of an experiment
Population-A population is any entire collection of people, animals, plants, or things that someone is interested in learning about. Each person or object in the population is called a member.
Probability- a ratio of the number of times an event occurs to the total number of times the activity is performed
Probability Model -A probability model is a mathematical representation of a chance process defined by its sample space, events within the sample space, and the assignment of a probability for each and every event.
Probability Simulation-A probability simulation is the use of a random number generator (e.g., spinners, coin toss, computers) to generate outcomes that are consistent with a given probability model.
- For example, to estimate the probability that a family with 4 children will include 3 or more boys, the children in a family might be represented by a sequence of four random digits with even digits representing a girl and odd digits representing a boy. This would generate “families” using a model that is consistent with a family having 4 children and each child being equally likely to be male or female. A large number of simulated “families” could be generated using technology, and then the relative frequency of those with 3 or more boys provides an estimate of the probability that a family with 4 children will include 3 or more boys.
Prediction- a decision or guess about something you can expect to happen
Random Sample -A random sample of size 𝑛 is a sample that is selected using a process that ensures that every different possible sample of size 𝑛 had the same chance of being selected as the sample. This selection process implies that every individual member of the population has the same chance of being included in the sample.
Relative Frequency- the frequency of data divided by the total number of data
Sample-A sample is any subset of a population.
Sample Space-the sample space of a chance process is the set of all possible outcomes.
- For example, the sample space for the experiment of rolling a die is the set {1, 2, 3, 4, 5, 6}.
Simulation- a model of an experiment that might be too difficult or time-consuming to perform
Statistical Inference-Statistical inference is the process of drawing conclusions about population parameters using sample statistics. In Grade 7, this can be described as “the process of drawing conclusions about populations using information from a sample of the population.”
Theoretical Probability- the ratio of the number of ways an event can occur to the total number of equally likely outcomes
Trial- each repetition or observation of an experiment
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