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## AP®︎/College Statistics

### Course: AP®︎/College Statistics>Unit 8

Lesson 1: Introduction to random variables and probability distributions

# Develop probability distributions: Theoretical probabilities

## Problem

A board game has players roll two dice — one $6$-sided and one $4$-sided — and subtract the numbers showing on the faces. The game only looks at non-negative differences. For example, if a player rolls a $1$ and a $4$, the difference is $3$.
Here is the sample space showing the possible (equally likely) outcomes of a single roll:
$\mathbf{1}$$\mathbf{2}$$\mathbf{3}$$\mathbf{4}$
$\mathbf{1}$$0$$1$$2$$3$
$\mathbf{2}$$1$$0$$1$$2$
$\mathbf{3}$$2$$1$$0$$1$
$\mathbf{4}$$3$$2$$1$$0$
$\mathbf{5}$$4$$3$$2$$1$
$\mathbf{6}$$5$$4$$3$$2$
Which graph represents the theoretical probability distribution of the differences?