There Are 228 Identical Plastic Chips Numbered 1 Through 228 In A Box. What Is The Probability Of Reaching Into The Box And Randomly Drawing A Chip Number That Is Smaller Than 117? Express Your Answer As A Simplified Fraction Or A Decimal Rounded To

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Introduction

When dealing with probability problems, it's essential to understand the concept of probability and how it relates to the given scenario. In this case, we have 228 identical plastic chips numbered 1 through 228 in a box. We want to find the probability of randomly drawing a chip number that is smaller than 117.

Understanding the Problem

To solve this problem, we need to understand the total number of possible outcomes and the number of favorable outcomes. The total number of possible outcomes is the total number of chips in the box, which is 228. The number of favorable outcomes is the number of chips that are smaller than 117.

Counting the Number of Favorable Outcomes

To count the number of chips that are smaller than 117, we can simply count the number of chips from 1 to 116, since these are the chips that are smaller than 117. Therefore, the number of favorable outcomes is 116.

Calculating the Probability

Now that we have the total number of possible outcomes and the number of favorable outcomes, we can calculate the probability of randomly drawing a chip number that is smaller than 117. The probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Probability = Number of favorable outcomes / Total number of possible outcomes Probability = 116 / 228

Simplifying the Fraction

To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 116 and 228 is 4. Therefore, we can simplify the fraction as follows:

Probability = (116 ÷ 4) / (228 ÷ 4) Probability = 29 / 57

Converting the Fraction to a Decimal

To convert the fraction to a decimal, we can divide the numerator by the denominator.

Probability = 29 ÷ 57 Probability ≈ 0.509

Conclusion

In conclusion, the probability of randomly drawing a chip number that is smaller than 117 from a box of 228 identical plastic chips is 29/57 or approximately 0.509.

Frequently Asked Questions

  • What is the probability of drawing a chip number that is greater than 117? The probability of drawing a chip number that is greater than 117 is 1 - (probability of drawing a chip number that is smaller than 117). Therefore, the probability is 1 - (29/57) = 28/57 or approximately 0.491.
  • What is the probability of drawing a chip number that is equal to 117? The probability of drawing a chip number that is equal to 117 is 1/228, since there is only one chip with the number 117.

Real-World Applications

Probability problems like this one have many real-world applications. For example, in quality control, manufacturers may want to know the probability of a product failing a certain test. In finance, investors may want to know the probability of a stock price increasing or decreasing. In medicine, doctors may want to know the probability of a patient recovering from a certain disease.

Tips and Tricks

  • When dealing with probability problems, it's essential to understand the concept of probability and how it relates to the given scenario.
  • To calculate the probability of an event, you need to know the total number of possible outcomes and the number of favorable outcomes.
  • You can simplify a fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
  • You can convert a fraction to a decimal by dividing the numerator by the denominator.

Further Reading

  • For more information on probability, see the following resources:
  • Khan Academy: Probability
  • Math Is Fun: Probability
  • Wolfram MathWorld: Probability

References

Introduction

In our previous article, we discussed the probability of drawing a chip number smaller than 117 from a box of 228 identical plastic chips. In this article, we will answer some frequently asked questions related to this topic.

Q&A

Q: What is the probability of drawing a chip number that is greater than 117?

A: The probability of drawing a chip number that is greater than 117 is 1 - (probability of drawing a chip number that is smaller than 117). Therefore, the probability is 1 - (29/57) = 28/57 or approximately 0.491.

Q: What is the probability of drawing a chip number that is equal to 117?

A: The probability of drawing a chip number that is equal to 117 is 1/228, since there is only one chip with the number 117.

Q: How do I calculate the probability of drawing a chip number that is smaller than 117?

A: To calculate the probability of drawing a chip number that is smaller than 117, you need to know the total number of possible outcomes and the number of favorable outcomes. The total number of possible outcomes is the total number of chips in the box, which is 228. The number of favorable outcomes is the number of chips that are smaller than 117, which is 116. The probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Probability = Number of favorable outcomes / Total number of possible outcomes Probability = 116 / 228

Q: Can I simplify the fraction 116/228?

A: Yes, you can simplify the fraction 116/228 by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 116 and 228 is 4. Therefore, you can simplify the fraction as follows:

Probability = (116 ÷ 4) / (228 ÷ 4) Probability = 29 / 57

Q: How do I convert the fraction 29/57 to a decimal?

A: To convert the fraction 29/57 to a decimal, you can divide the numerator by the denominator.

Probability = 29 ÷ 57 Probability ≈ 0.509

Q: What is the real-world application of this problem?

A: Probability problems like this one have many real-world applications. For example, in quality control, manufacturers may want to know the probability of a product failing a certain test. In finance, investors may want to know the probability of a stock price increasing or decreasing. In medicine, doctors may want to know the probability of a patient recovering from a certain disease.

Q: What are some tips and tricks for solving probability problems?

A: Here are some tips and tricks for solving probability problems:

  • When dealing with probability problems, it's essential to understand the concept of probability and how it relates to the given scenario.
  • To calculate the probability of an event, you need to know the total number of possible outcomes and the number of favorable outcomes.
  • You can simplify a fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
  • You can convert a fraction to a decimal by dividing the numerator by the denominator.

Conclusion

In conclusion, the probability of drawing a chip number smaller than 117 from a box of 228 identical plastic chips is 29/57 or approximately 0.509. We hope this article has helped you understand the concept of probability and how to solve probability problems.

Frequently Asked Questions

  • What is the probability of drawing a chip number that is greater than 117?
  • What is the probability of drawing a chip number that is equal to 117?
  • How do I calculate the probability of drawing a chip number that is smaller than 117?
  • Can I simplify the fraction 116/228?
  • How do I convert the fraction 29/57 to a decimal?
  • What is the real-world application of this problem?
  • What are some tips and tricks for solving probability problems?

Further Reading

  • For more information on probability, see the following resources:
  • Khan Academy: Probability
  • Math Is Fun: Probability
  • Wolfram MathWorld: Probability

References