Math Problem Statement
Solution of 2nd
Solution of 2nd
Solution
To solve question 2, which involves writing the sample space for rolling two dice, here is the explanation and solution:
Solution to Question 2:
When two dice are rolled, each die has 6 faces numbered from 1 to 6. The outcomes for the two dice can be represented as ordered pairs , where:
- represents the outcome of the first die.
- represents the outcome of the second die.
The total number of outcomes is .
Sample Space (S):
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), \\ (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), \\ (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), \\ (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), \\ (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)\}$$ --- Would you like a more detailed explanation or visualization of this sample space? --- **Expanding questions related to this solution:** 1. How can we determine the probability of getting a sum of 7 when two dice are rolled? 2. What is the probability of rolling doubles (e.g., $$(1, 1), (2, 2)$$) with two dice? 3. If one die is biased to favor even numbers, how does the sample space or probabilities change? 4. How do we calculate the number of outcomes for rolling three dice instead of two? 5. Can the outcomes of rolling two dice be represented using a tree diagram? **Tip:** When working with probabilities involving dice, always start by identifying all possible outcomes to ensure calculations are based on the complete sample space.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Probability
Sample Space
Combinatorics
Formulas
Total outcomes = 6 * 6 = 36
Theorems
Counting principle
Probability principle
Suitable Grade Level
Grades 6-8