Kellie Randomly Chooses A Number From 1 To 10. What Is The Probability She Chooses A Number Less Than 3?A. 1 5 \frac{1}{5} 5 1 ​ B. 3 10 \frac{3}{10} 10 3 ​ C. 4 5 \frac{4}{5} 5 4 ​ D. 2 9 \frac{2}{9} 9 2 ​

Introduction

Probability is a fundamental concept in mathematics that deals with the likelihood of an event occurring. In this article, we will explore a simple yet interesting problem involving probability, which is randomly choosing a number from 1 to 10. Our goal is to determine the probability that Kellie chooses a number less than 3.

What is Probability?

Probability is a measure of the likelihood of an event occurring. It is usually expressed as a value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. In this case, we want to find the probability that Kellie chooses a number less than 3.

The Sample Space

The sample space is the set of all possible outcomes in an experiment. In this case, the sample space consists of the numbers 1 to 10. There are 10 possible outcomes, and each outcome is equally likely.

The Event

The event is the set of outcomes that we are interested in. In this case, the event is choosing a number less than 3. This means that the event consists of the numbers 1 and 2.

Counting the Number of Outcomes

To find the probability of the event, we need to count the number of outcomes that are in the event. In this case, there are 2 outcomes that are in the event: 1 and 2.

Calculating the Probability

The probability of an event is calculated by dividing the number of outcomes in the event by the total number of outcomes in the sample space. In this case, the probability of choosing a number less than 3 is:

$$P(\text{less than 3}) = \frac{\text{number of outcomes in the event}}{\text{total number of outcomes in the sample space}}$$

$$P(\text{less than 3}) = \frac{2}{10}$$

$$P(\text{less than 3}) = \frac{1}{5}$$

Conclusion

In conclusion, the probability that Kellie chooses a number less than 3 is $\frac{1}{5}$. This means that there is a 20% chance that Kellie will choose a number less than 3.

Simplifying the Fraction

The fraction $\frac{1}{5}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1. Therefore, the simplified fraction is still $\frac{1}{5}$.

Comparing with Other Options

Let's compare our answer with the other options:

• Option A: $\frac{1}{5}$
• Option B: $\frac{3}{10}$
• Option C: $\frac{4}{5}$
• Option D: $\frac{2}{9}$

Our answer, $\frac{1}{5}$, is the same as Option A. Therefore, the correct answer is:

The Correct Answer

The correct answer is:

A. $\frac{1}{5}$

Final Thoughts

Introduction

In our previous article, we explored a simple problem involving probability, where Kellie randomly chooses a number from 1 to 10. We determined that the probability of her choosing a number less than 3 is $\frac{1}{5}$. In this article, we will answer some frequently asked questions related to this problem.

Q&A

Q: What is the probability of Kellie choosing a number greater than 3?

A: To find the probability of Kellie choosing a number greater than 3, we need to count the number of outcomes that are greater than 3 and divide it by the total number of outcomes in the sample space. There are 7 outcomes that are greater than 3 (4, 5, 6, 7, 8, 9, and 10). Therefore, the probability of Kellie choosing a number greater than 3 is:

$$P(\text{greater than 3}) = \frac{7}{10}$$

Q: What is the probability of Kellie choosing an even number?

A: To find the probability of Kellie choosing an even number, we need to count the number of even outcomes and divide it by the total number of outcomes in the sample space. There are 5 even outcomes (2, 4, 6, 8, and 10). Therefore, the probability of Kellie choosing an even number is:

$$P(\text{even}) = \frac{5}{10}$$

Q: What is the probability of Kellie choosing a number between 5 and 7?

A: To find the probability of Kellie choosing a number between 5 and 7, we need to count the number of outcomes that are between 5 and 7 and divide it by the total number of outcomes in the sample space. There are 2 outcomes that are between 5 and 7 (6 and 7). Therefore, the probability of Kellie choosing a number between 5 and 7 is:

$$P(\text{between 5 and 7}) = \frac{2}{10}$$

Q: What is the probability of Kellie choosing a number that is not 1 or 2?

A: To find the probability of Kellie choosing a number that is not 1 or 2, we need to count the number of outcomes that are not 1 or 2 and divide it by the total number of outcomes in the sample space. There are 8 outcomes that are not 1 or 2 (3, 4, 5, 6, 7, 8, 9, and 10). Therefore, the probability of Kellie choosing a number that is not 1 or 2 is:

$$P(\text{not 1 or 2}) = \frac{8}{10}$$

Q: What is the probability of Kellie choosing a number that is greater than 5 and less than 8?

A: To find the probability of Kellie choosing a number that is greater than 5 and less than 8, we need to count the number of outcomes that are greater than 5 and less than 8 and divide it by the total number of outcomes in the sample space. There are 2 outcomes that are greater than 5 and less than 8 (6 and 7). Therefore, the probability of Kellie choosing a number that is greater than 5 and less than 8 is:

$$P(\text{greater than 5 and less than 8}) = \frac{2}{10}$$

Conclusion

In this article, we answered some frequently asked questions related to the problem of Kellie randomly choosing a number from 1 to 10. We calculated the probabilities of various events, including choosing a number greater than 3, an even number, a number between 5 and 7, a number that is not 1 or 2, and a number that is greater than 5 and less than 8. We hope that this article has provided a clear understanding of probability and how to calculate it.

Final Thoughts

Probability is a fundamental concept in mathematics that deals with the likelihood of an event occurring. In this article, we explored a simple problem involving probability and calculated the probabilities of various events. We hope that this article has provided a clear understanding of probability and how to calculate it.