November 11, 2016

This lesson is designed to introduce students to random numbers and fairness as a precursor to learning about probability. The lesson provides links to discussions and activities related to probability and fairness as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with this one.

- Mathematics > General

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Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.

Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.

Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model.

(+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.

(+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).