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Chapter 9: Problem 11

If a die is rolled, in how many ways can an odd number come up?

Short Answer

Expert verified
There are 3 ways an odd number can come up.

Step by step solution

01

- Understand the die

A standard die has 6 faces, numbered from 1 to 6. Identify these numbers: 1, 2, 3, 4, 5, and 6.
02

- Identify the odd numbers

From the numbers on the die, pick out which ones are odd. The odd numbers among 1, 2, 3, 4, 5, and 6 are 1, 3, and 5.
03

- Count the odd numbers

Now count how many odd numbers are there. The odd numbers identified are 1, 3, and 5, which makes a total of 3 odd numbers.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

rolling a die
Rolling a die is a common example used to explain basic probability. A standard die, or dice, has six faces. Each face shows a different number from 1 to 6. When you roll the die, any one of these six numbers can come up. The numbers are equally likely to appear because the die is fair, meaning each number has the same chance of being rolled. This concept is foundational in learning about probability and outcomes because it is easy to visualize and understand.
odd numbers
Odd numbers are integers that cannot be divided evenly by 2. In simpler terms, their final digit is either 1, 3, 5, 7, or 9. When you roll a standard die, you get the numbers 1, 2, 3, 4, 5, and 6. Among these, the odd numbers are 1, 3, and 5. Learning to identify odd and even numbers is an important step in understanding outcomes in probability. This helps differentiate between the possible results based on specific criteria.
counting outcomes
Counting outcomes means identifying how many possible results match a given condition. In our case, we want to know how many ways an odd number can come up when rolling a die. First, identify the odd numbers on the die: 1, 3, and 5. Then, count these numbers. There are three odd numbers (1, 3, and 5), so there are three possible outcomes where an odd number comes up. Understanding how to count outcomes helps in calculating probabilities accurately.
basic probability
Basic probability measures the chance of a specific event happening. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, the probability that you roll an odd number with a die is found by counting the odd numbers (favorable outcomes) and dividing by the total number of faces on the die (possible outcomes). For a standard die, there are 3 odd numbers (1, 3, and 5) and 6 total numbers (1, 2, 3, 4, 5, and 6). So, the probability is: \[\text{Probability} = \frac{3\text{ (odd numbers)}}{6\text{ (total numbers)}} = \frac{1}{2}\]. This means there is a 1 in 2, or 50%, chance of rolling an odd number.

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