Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
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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