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## Precalculus

### Unit 8: Lesson 7

Theoretical & empirical probability distributions

# Develop probability distributions: Theoretical probabilities

AP.STATS: VAR‑5 (EU), VAR‑5.A (LO), VAR‑5.A.1 (EK), VAR‑5.A.2 (EK), VAR‑5.A.3 (EK) CCSS.Math: HSS.MD.A.3

## 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:
start subscript, 1, start superscript, start text, s, t, end text, end superscript, start text, space, d, i, e, end text, end subscript, \diagdown, start superscript, 2, start superscript, start text, n, d, end text, end superscript, start text, space, d, i, e, end text, end superscript1234
10123
21012
32101
43210
54321
65432
Which graph represents the theoretical probability distribution of the differences?