The Spinner Is Divided Into 10 Equal Sections.Which Event Has A Theoretical Probability Of Exactly 1 5 \frac{1}{5} 5 1 ​ ? Select Three Options.- Spinning A Number Less Than 3- Spinning A 4 Or 5- Spinning An Odd Number

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Introduction

Probability is a fundamental concept in mathematics that helps us understand the likelihood of events occurring. In this discussion, we will explore the concept of theoretical probability and apply it to a spinner divided into 10 equal sections. We will examine three options and determine which one has a theoretical probability of exactly 15\frac{1}{5}.

The Spinner

The spinner is divided into 10 equal sections, numbered from 1 to 10. Each section represents a possible outcome when the spinner is spun. The spinner is a classic example of a random event, where the outcome is uncertain and can be influenced by various factors.

Theoretical Probability

Theoretical probability is a measure of the likelihood of an event occurring, based on the number of favorable outcomes divided by the total number of possible outcomes. In the case of the spinner, the total number of possible outcomes is 10, since there are 10 sections.

Option 1: Spinning a Number Less Than 3

Let's consider the first option: spinning a number less than 3. This includes the numbers 1 and 2. There are 2 favorable outcomes (1 and 2) out of a total of 10 possible outcomes. Therefore, the theoretical probability of spinning a number less than 3 is:

210=15\frac{2}{10} = \frac{1}{5}

Option 2: Spinning a 4 or 5

The second option is spinning a 4 or 5. There are 2 favorable outcomes (4 and 5) out of a total of 10 possible outcomes. Therefore, the theoretical probability of spinning a 4 or 5 is:

210=15\frac{2}{10} = \frac{1}{5}

Option 3: Spinning an Odd Number

The third option is spinning an odd number. This includes the numbers 1, 3, 5, 7, and 9. There are 5 favorable outcomes (1, 3, 5, 7, and 9) out of a total of 10 possible outcomes. Therefore, the theoretical probability of spinning an odd number is:

510=12\frac{5}{10} = \frac{1}{2}

Conclusion

Based on the calculations above, we can see that both options 1 and 2 have a theoretical probability of exactly 15\frac{1}{5}. However, option 3 has a theoretical probability of 12\frac{1}{2}, which is not equal to 15\frac{1}{5}.

Recommendation

Therefore, the correct answer is options 1 and 2: spinning a number less than 3 and spinning a 4 or 5. Both of these options have a theoretical probability of exactly 15\frac{1}{5}.

Key Takeaways

  • Theoretical probability is a measure of the likelihood of an event occurring, based on the number of favorable outcomes divided by the total number of possible outcomes.
  • The spinner is a classic example of a random event, where the outcome is uncertain and can be influenced by various factors.
  • Options 1 and 2 have a theoretical probability of exactly 15\frac{1}{5}, while option 3 has a theoretical probability 12\frac{1}{2}.

Further Reading

For more information on probability and theoretical probability, please refer to the following resources:

  • Khan Academy: Probability
  • Math Is Fun: Probability
  • Wolfram MathWorld: Probability

References

Introduction

In our previous article, we explored the concept of theoretical probability and applied it to a spinner divided into 10 equal sections. We determined that options 1 and 2: spinning a number less than 3 and spinning a 4 or 5, both have a theoretical probability of exactly 15\frac{1}{5}. In this article, we will answer some frequently asked questions related to the spinner and theoretical probability.

Q&A

Q: What is the total number of possible outcomes when the spinner is spun?

A: The total number of possible outcomes is 10, since there are 10 sections on the spinner.

Q: What is the definition of theoretical probability?

A: Theoretical probability is a measure of the likelihood of an event occurring, based on the number of favorable outcomes divided by the total number of possible outcomes.

Q: How do you calculate the theoretical probability of an event?

A: To calculate the theoretical probability of an event, you need to count the number of favorable outcomes and divide it by the total number of possible outcomes.

Q: What is the difference between theoretical probability and experimental probability?

A: Theoretical probability is a measure of the likelihood of an event occurring, based on the number of favorable outcomes divided by the total number of possible outcomes. Experimental probability, on the other hand, is a measure of the likelihood of an event occurring, based on the number of times the event occurs in a series of trials.

Q: Can you give an example of how to calculate the theoretical probability of an event?

A: Let's say we want to calculate the theoretical probability of spinning a 4 or 5 on the spinner. There are 2 favorable outcomes (4 and 5) out of a total of 10 possible outcomes. Therefore, the theoretical probability of spinning a 4 or 5 is:

210=15\frac{2}{10} = \frac{1}{5}

Q: What is the relationship between the number of favorable outcomes and the total number of possible outcomes?

A: The number of favorable outcomes is a subset of the total number of possible outcomes. In other words, the number of favorable outcomes is always less than or equal to the total number of possible outcomes.

Q: Can you give an example of how to use the spinner to demonstrate the concept of theoretical probability?

A: Let's say we want to demonstrate the concept of theoretical probability by spinning the spinner 10 times and counting the number of times we spin a 4 or 5. We can then calculate the experimental probability of spinning a 4 or 5 by dividing the number of times we spin a 4 or 5 by the total number of trials.

Q: What is the importance of understanding theoretical probability?

A: Understanding theoretical probability is important because it helps us make informed decisions in a variety of situations, such as predicting the outcome of a game or making a decision based on probability.

Conclusion

In this article, we answered some frequently asked questions related to the spinner and theoretical probability. We hope that this article has helped you understand the concept of theoretical probability and how it can be applied to real-world situations.

Key Takeaways

  • Theoretical probability is a measure of the likelihood of an event occurring, based on the number of favorable outcomes divided by the total number of possible outcomes.
  • The spinner is a classic example of a random event, where the outcome is uncertain and can be influenced by various factors.
  • Understanding theoretical probability is important because it helps us make informed decisions in a variety of situations.

Further Reading

For more information on probability and theoretical probability, please refer to the following resources:

  • Khan Academy: Probability
  • Math Is Fun: Probability
  • Wolfram MathWorld: Probability

References