# Binomial Probability Context Rich Problem

This material is replicated on a number of sites
as part of the
SERC Pedagogic Service Project

Initial Publication Date: March 29, 2012

## Summary

This activity consists of a single scenario-based problem allowing students to apply the binomial probability distribution to decide whether or not an outcome is likely random.

## Learning Goals

Students will be able to apply the binomial probability distribution in a realistic setting.

## Context for Use

This activity is appropriate for a introductory level business statistics course. It is appropriate for use in any size class. It can be used either to introduce the concepts of the binomial distribution, or to assess students' understanding after the binomial distribution has been discussed. If the problem is done in class it will take about 10-15 minutes to complete.

## Description and Teaching Materials

You are watching an episode of Law and Order. The plot for this episode includes a scientist that was trying to communicate with patients in a persistent vegetative state. She put two signs in front of the patients. The sign on the right side of the patient read 'Yes.' The sign on the left side of the patient read 'No.' Then she asked the patients yes or no questions and recorded their response as a 'Yes' if the patient first looked to the right, or a 'No' if the patient first looked to the left. In the show there is a disagreement over whether or not the scientist was actually communicating with these patients, or if she was simply recording random eye movements in these patients. The scientist claimed the percent of correct responses she got showed she was able to communicate with these patients. What percent of correct responses do you believe she should have gotten in order to claim she was able to communicate with the patients? Why?

The text of the problem can be downloaded below:

Probability Context Rich Problem (Microsoft Word 2007 (.docx) 11kB Mar14 12)

## Teaching Notes and Tips

This activity can be done in class individually or in small groups. It can also be assigned as a homework problem or as an exam question.

Students need to have some familiarity with the binomial probability distribution to successfully complete the problem. If your students are new to context-rich problems, you may want to include prompts to help students, such as 'What probability distribution is best suited to a situation like this one?'

Alternatively, you could use this problem as a Just-In-Time Teaching problem. You should expect to see students attempting to apply a wide variety of probability rules. Class discussion can focus on what types of questions are answered with the probability rules they have applied and how these questions differ from the one posed.

Students need to have some familiarity with the binomial probability distribution to successfully complete the problem. If your students are new to context-rich problems, you may want to include prompts to help students, such as 'What probability distribution is best suited to a situation like this one?'

Alternatively, you could use this problem as a Just-In-Time Teaching problem. You should expect to see students attempting to apply a wide variety of probability rules. Class discussion can focus on what types of questions are answered with the probability rules they have applied and how these questions differ from the one posed.

## Assessment

The purpose of the assessment will determine whether or not you need a rubric. If the problem will be graded, it may be helpful to give the students a rubric such as:

- Grade=A: All statistical reasoning in the answer is correct. All relevant calculations are included. May have 1-2 minor mistakes, such as a minor error in a calculation.
- Grade=B: Statistical reasoning in the answer is correct, but the answer contains 3-4 minor mistakes such as calculation errors.
- Grade=C: Contains significant errors in the statistical reasoning, such as missing steps in the problem solving process, or several significant errors in calculations.
- Grade=D: Very little of the statistical reasoning is correct and relevant to the problem.

- Grade=F: None of the economic content is relevant to the question.