Math Problem Statement
Solution
Let’s analyze the question presented in the image:
Problem Statement:
A single die is rolled three separate times. How many ways can you roll:
- A number less than 5,
- Then an even number,
- Then an odd number?
Step-by-Step Solution:
-
First roll: A number less than 5
The numbers less than 5 on a standard die are {1, 2, 3, 4}.
There are 4 possible outcomes for this roll. -
Second roll: An even number
The even numbers on a die are {2, 4, 6}.
There are 3 possible outcomes for this roll. -
Third roll: An odd number
The odd numbers on a die are {1, 3, 5}.
There are 3 possible outcomes for this roll.
Total Number of Ways:
To find the total number of ways to satisfy all three conditions, multiply the possibilities for each roll:
Final Answer:
There are 36 ways to roll a number less than 5, then an even number, and then an odd number.
Let me know if you need further clarification!
Here are 5 follow-up questions to expand your understanding:
- What is the probability of rolling a specific sequence (e.g., 3, 4, 1) under these conditions?
- How would the answer change if the die had 8 sides instead of 6?
- What if the condition for the second roll was "greater than 3" instead of "even"?
- How many outcomes are possible if there are no conditions for the rolls?
- Can you represent these outcomes as an organized list?
Tip: Always start by identifying valid outcomes for each condition and systematically multiply them to find the total combinations.
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Math Problem Analysis
Mathematical Concepts
Probability
Combinatorics
Formulas
Total combinations = Product of valid outcomes for each condition
Theorems
Fundamental principle of counting
Suitable Grade Level
Grades 6-8