3) Rolling three four-sided dice twice, what is the probability of the second total being larger than the first?

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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**Problem 3: Probability Calculation**

**Question:**
Rolling three four-sided dice twice, what is the probability of the second total being larger than the first?

**Explanation:**
This problem involves understanding probability with multiple dice rolls. You are asked to calculate the likelihood that, after rolling three four-sided dice two times, the sum of the numbers on the second roll is greater than the sum of the numbers on the first roll.

**Key Concepts:**
- Each four-sided die produces outcomes numbered from 1 to 4.
- When you roll three such dice, the possible outcomes range from 3 (all dice show 1) to 12 (all dice show 4).
- You need to compare the outcomes of two series of rolls and determine the probability that the second series yields a higher total than the first.
Transcribed Image Text:**Problem 3: Probability Calculation** **Question:** Rolling three four-sided dice twice, what is the probability of the second total being larger than the first? **Explanation:** This problem involves understanding probability with multiple dice rolls. You are asked to calculate the likelihood that, after rolling three four-sided dice two times, the sum of the numbers on the second roll is greater than the sum of the numbers on the first roll. **Key Concepts:** - Each four-sided die produces outcomes numbered from 1 to 4. - When you roll three such dice, the possible outcomes range from 3 (all dice show 1) to 12 (all dice show 4). - You need to compare the outcomes of two series of rolls and determine the probability that the second series yields a higher total than the first.
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