# Connexions

You are here: Home » Content » Probability Topics: Probability Lab (edited: Teegarden)

### Recently Viewed

This feature requires Javascript to be enabled.

# Probability Topics: Probability Lab (edited: Teegarden)

Module by: Mary Teegarden. E-mail the author

Summary: This module presents students with a lab exercise allowing them to apply their understanding of Probability. In an experiment using M&Ms candies, students will calculate and compare the theoretical and empirical probabilities of drawing particular color candies at random, with and without replacement. Labs changed to incorporate mini-tabs.

Note: You are viewing an old version of this document. The latest version is available here.

Class time:

Name:

## Student Learning Outcomes:

• The student will calculate theoretical and empirical probabilities.
• The student will appraise the differences between the two types of probabilities.
• The student will demonstrate an understanding of long-term probabilities.

## Sum of Two Dice

Begin by looking at Theoretical probabilities for the sum of two dice. Let the value in the first row be the result for Die 1 and the value in the first column be the value for Die 2. Input the sum of the corresponding row and column in each box.

 + 1 2 3 4 5 6 1 2 3 4 5 6
 Sum Count Probability 2 3 4 5 6 7 8 9 10 11 12

## Theoretical Probabilities

1. P(sum less than 5) = _________________
2. P(sum at least 9) = _________________
3. P(sum at most 6) = _________________
4. P(sum more than 7) = _________________
5. P(sum between 3 and 8) = _________________
6. P(sum less than 11) = _________________

## Do the Experiment:

### Rolling the dice

Using Minitab, simulate rolling two dice 500 times and finding the sum. Use Calc -> Random Data -> Integer, 360 rows and save in die 1, die 2. Then use the Calc -> Row Statistics. Select Sum, the two die columns and save in Sum Then use Stat -> Tables -> Tally to summarize the data. Be sure to select all four options.

Table 3: Emperical Probabilities
Sum Quantity Probability
2
3
4
5
6
7
8
9
10
11
12

## Emperical Probabilities

1. P(sum less than 5) = _________________
2. P(sum at least 9) = _________________
3. P(sum at most 6) = _________________
4. P(sum more than 7) = _________________
5. P(sum between 3 and 8) = _________________
6. P(sum less than 11) = _________________

## Essay Questions

1. How do the empirical probabilities compare to the theoretical probabiliies?
2. If you increased the number of times you rolled the dice to 720, would the empirical probability values change? Rerun the simulation and record your results.
3. Did the increase in trials (see (2) above) cause the empirical probabilities and theoretical probabilities to be closer together or farther apart? Why?

## Content actions

### Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks