### Mathematics lessons for IB® Diploma Programme

Analysis and Approaches | Probability and Statistics

## Tossing Dice

### Activity Overview

This lesson involves simulating tossing two fair dice, recording the sum of the faces, and creating a dotplot of the sums.

As a result, students will:

• Observe how the simulated sampling distribution for the sums of the faces changes as the number of samples is increased.
• Compare their distribution of the sums of the faces of two randomly-tossed dice to their classmates' distributions, and observe how the distributions are alike and how they differ.
• Answer probability questions based on a dotplot of the sums of the faces of two randomly-tossed fair dice.
• Compare the distribution of the sums of the faces from two randomly-tossed fair dice to the theoretical distribution for the sums of the faces.

### Objectives

• Students will estimate the probability of outcomes from a dotplot.
• Students will compare a simulated sampling distribution to the theoretical distribution for the underlying relationship and note that the simulated distribution will more closely approximate the theoretical after a large number of samples.

### Vocabulary

• dice
• dotplot
• faces of a die
• probability of an outcome
• simulated sampling distribution
• theoretical distribution