Answered: We throw three independent fair dice.…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

We throw three independent fair dice. Find the probability that the sum of the outcomes is equal to 10.

Expert Solution

Step 1

When die is rolled, there would be 6 possible outcomes $\{1, 2, 3, 4, 5, 6\}$ . For drawing three independent dice there would be $6^{3} = 216$ possible outcomes.

The outcomes that the sum is equal to 10 is,

$\{\begin{matrix} (1, 3, 6) & (1, 4, 5) & (1, 5, 4) & (1, 6, 3) \\ (2, 2, 6) & (2, 3, 5) & (2, 4, 4) & (2, 5, 3) & (2, 6, 2) \\ (3, 1, 6) & (3, 2, 5) & (3, 3, 4) & (3, 4, 3) & (3, 5, 2) & (3, 6, 1) \\ (4, 1, 5) & (4, 2, 4) & (4, 3, 3) & (4, 4, 2) & (4, 5, 1) \\ (5, 1, 4) & (5, 2, 3) & (5, 3, 2) & (5, 4, 1) \\ (6, 1, 3) & (6, 2, 2) & (6, 3, 1) \end{matrix}\} \begin{matrix} \end{matrix}$