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5. In an experiment of rolling two dice what is the probability of not getting the same number on both dice.

5. In an experiment of rolling two dice what is the probability of not getting the same number on both dice.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
ChapterCSR: Contents Of Student Resources
Section: Chapter Questions
Problem 11.22EP
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Question
**Problem 5** In an experiment of rolling two dice, what is the probability of not getting the same number on both dice? **Solution:** To solve this problem, we will find the total number of possible outcomes and the number of outcomes where the two dice do not show the same number. 1. **Total Possible Outcomes:** - Each die has 6 faces, so when rolling two dice, the total number of outcomes is \(6 \times 6 = 36\). 2. **Outcomes of Rolling the Same Number:** - The numbers can be the same when both dice show any of the following pairs: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6). - This results in 6 outcomes where the numbers are the same. 3. **Outcomes of Rolling Different Numbers:** - To find the number of outcomes with different numbers, subtract the same-number outcomes (6) from the total outcomes (36). - Therefore, there are \(36 - 6 = 30\) outcomes where the numbers on the two dice are different. 4. **Probability:** - The probability of rolling different numbers is the number of different-number outcomes divided by the total number of outcomes. - Probability = \(\frac{30}{36} = \frac{5}{6}\). Therefore, the probability of not getting the same number on both dice is \(\frac{5}{6}\).
Transcribed Image Text:**Problem 5** In an experiment of rolling two dice, what is the probability of not getting the same number on both dice? **Solution:** To solve this problem, we will find the total number of possible outcomes and the number of outcomes where the two dice do not show the same number. 1. **Total Possible Outcomes:** - Each die has 6 faces, so when rolling two dice, the total number of outcomes is \(6 \times 6 = 36\). 2. **Outcomes of Rolling the Same Number:** - The numbers can be the same when both dice show any of the following pairs: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6). - This results in 6 outcomes where the numbers are the same. 3. **Outcomes of Rolling Different Numbers:** - To find the number of outcomes with different numbers, subtract the same-number outcomes (6) from the total outcomes (36). - Therefore, there are \(36 - 6 = 30\) outcomes where the numbers on the two dice are different. 4. **Probability:** - The probability of rolling different numbers is the number of different-number outcomes divided by the total number of outcomes. - Probability = \(\frac{30}{36} = \frac{5}{6}\). Therefore, the probability of not getting the same number on both dice is \(\frac{5}{6}\).
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