Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 12 - Counting and Probability - Section 12.3 Probability - 12.3 Assess Your Understanding - Page 885: 41



Work Step by Step

We know that probability of an event $E$ is given by the formula: $P(E)=\dfrac{\text{number of favorable outcomes}}{\text{number of all outcomes}}$ The generalized basic counting principle says that if an event $e_1$ can be performed in $n_1$ different ways and an event $e_2$ can be performed in $n_2$ different ways, then there are $n_1\cdot n_2$ different ways of performing them together. This can easily be extended to $n$ events. Since a die has $6$ sides with $6$ different numbers, then there are $6$ possible outcomes when one die is rolled. Hence, when two dice are rolled, there are $6\cdot6=36$ possible outcomes. Out of these, the outcomes that have a sum of $7$ are: $(1,6),(2,5),(3,4),(4,3),(5,2),(6,1).$ ($6$ favorable outcomes) Thus, $P(\text{sum is 7})=\dfrac{6}{36}=\dfrac{1}{6}$
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