Math Problem Statement

A single die is rolled three separate times. How many ways can you roll a number less than 5, then an even, and then an odd?

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:

  1. A number less than 5,
  2. Then an even number,
  3. Then an odd number?

Step-by-Step Solution:

  1. 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.

  2. Second roll: An even number
    The even numbers on a die are {2, 4, 6}.
    There are 3 possible outcomes for this roll.

  3. 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: 4×3×3=364 \times 3 \times 3 = 36


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:

  1. What is the probability of rolling a specific sequence (e.g., 3, 4, 1) under these conditions?
  2. How would the answer change if the die had 8 sides instead of 6?
  3. What if the condition for the second roll was "greater than 3" instead of "even"?
  4. How many outcomes are possible if there are no conditions for the rolls?
  5. 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