A Box Contains Cards That Are Numbered From 1 To 100. What Is The Probability Of Randomly Selecting A Number That Is Less Than $12$?A. $\frac{1}{100}$B. \$\frac{1}{12}$[/tex\]C. $\frac{11}{100}$D.

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Introduction

Probability is a fundamental concept in mathematics that deals with the likelihood of an event occurring. It is a measure of the chance or uncertainty associated with a particular outcome. In this article, we will explore the concept of probability and how it is applied to real-world problems. We will also discuss the probability of randomly selecting a number that is less than 12 from a box containing cards numbered from 1 to 100.

What is Probability?

Probability is a numerical value between 0 and 1 that represents the likelihood of an event occurring. It is calculated as the number of favorable outcomes divided by the total number of possible outcomes. For example, if we have a fair six-sided die, the probability of rolling a 6 is 1/6, because there is one favorable outcome (rolling a 6) out of six possible outcomes (rolling a 1, 2, 3, 4, 5, or 6).

Calculating Probability

To calculate the probability of an event, we need to know the number of favorable outcomes and the total number of possible outcomes. The formula for probability is:

P(E) = Number of favorable outcomes / Total number of possible outcomes

Where P(E) is the probability of the event E.

The Problem

A box contains cards that are numbered from 1 to 100. What is the probability of randomly selecting a number that is less than 12?

Step 1: Identify the Number of Favorable Outcomes

The number of favorable outcomes is the number of cards that are less than 12. Since the cards are numbered from 1 to 100, the number of cards that are less than 12 is 11 (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11).

Step 2: Identify the Total Number of Possible Outcomes

The total number of possible outcomes is the total number of cards in the box, which is 100.

Step 3: Calculate the Probability

Now that we have the number of favorable outcomes and the total number of possible outcomes, we can calculate the probability using the formula:

P(E) = Number of favorable outcomes / Total number of possible outcomes = 11 / 100 = 0.11

Conclusion

The probability of randomly selecting a number that is less than 12 from a box containing cards numbered from 1 to 100 is 11/100 or 0.11.

Comparison with Answer Choices

Let's compare our answer with the answer choices:

A. 1/100 = 0.01 (This is incorrect, because the probability is not 1/100.)

B. 1/12 = 0.083 (This is incorrect, because the probability is not 1/12.)

C. 11/100 = 0.11 (This is correct, because the probability is 11/100.)

D. (This answer choice is not provided.)

Real-World Applications

Probability is used in many real-world applications, such as:

  • Insurance: Probability is used to calculate the likelihood of an event occurring, such as a car accident or a natural disaster.
  • Finance: Probability is used to calculate the likelihood of a stock or a bond performing well.
  • Medicine: Probability is used to calculate the likelihood of a patient responding to a treatment.
  • Engineering: Probability is used to calculate the likelihood of a system failing or performing well.

Conclusion

In conclusion, probability is a fundamental concept in mathematics that deals with the likelihood of an event occurring. It is a measure of the chance or uncertainty associated with a particular outcome. We have discussed the probability of randomly selecting a number that is less than 12 from a box containing cards numbered from 1 to 100. We have also compared our answer with the answer choices and discussed the real-world applications of probability.

Frequently Asked Questions

  • What is probability?
  • How is probability calculated?
  • What are the real-world applications of probability?

Answers

  • Probability is a numerical value between 0 and 1 that represents the likelihood of an event occurring.
  • Probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes.
  • The real-world applications of probability include insurance, finance, medicine, and engineering.

Glossary

  • Probability: A numerical value between 0 and 1 that represents the likelihood of an event occurring.
  • Favorable outcomes: The number of outcomes that are in our favor.
  • Total number of possible outcomes: The total number of outcomes that are possible.
  • Event: A specific outcome or set of outcomes.

References

  • "Probability" by Khan Academy
  • "Probability" by Math Is Fun
  • "Probability" by Wikipedia
    Probability Q&A: Frequently Asked Questions =====================================================

Introduction

Probability is a fundamental concept in mathematics that deals with the likelihood of an event occurring. It is a measure of the chance or uncertainty associated with a particular outcome. In this article, we will answer some frequently asked questions about probability.

Q: What is probability?

A: Probability is a numerical value between 0 and 1 that represents the likelihood of an event occurring. It is a measure of the chance or uncertainty associated with a particular outcome.

Q: How is probability calculated?

A: Probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes. The formula for probability is:

P(E) = Number of favorable outcomes / Total number of possible outcomes

Where P(E) is the probability of the event E.

Q: What are the different types of probability?

A: There are two main types of probability:

  • Theoretical probability: This is the probability of an event occurring based on the number of favorable outcomes and the total number of possible outcomes.
  • Experimental probability: This is the probability of an event occurring based on the results of repeated trials or experiments.

Q: What is the difference between probability and chance?

A: Probability and chance are related but distinct concepts. Probability is a numerical value that represents the likelihood of an event occurring, while chance is a more general term that refers to the uncertainty or unpredictability of an event.

Q: How is probability used in real-world applications?

A: Probability is used in many real-world applications, such as:

  • Insurance: Probability is used to calculate the likelihood of an event occurring, such as a car accident or a natural disaster.
  • Finance: Probability is used to calculate the likelihood of a stock or a bond performing well.
  • Medicine: Probability is used to calculate the likelihood of a patient responding to a treatment.
  • Engineering: Probability is used to calculate the likelihood of a system failing or performing well.

Q: What are some common probability formulas?

A: Some common probability formulas include:

  • P(E) = Number of favorable outcomes / Total number of possible outcomes
  • P(E) = 1 - P(E') (where P(E') is the probability of the event E' not occurring)
  • P(E ∪ F) = P(E) + P(F) - P(E ∩ F) (where P(E ∪ F) is the probability of the event E or F occurring, and P(E ∩ F) is the probability of the event E and F occurring)

Q: What is the concept of independent events?

A: Independent events are events that do not affect each other. The probability of one event occurring does not affect the probability of the other event occurring.

Q: What is the concept of dependent events?

A: Dependent events are events that affect each other. The probability of one event occurring affects the probability of the other event occurring.

Q: What is the concept of conditional probability?

A: Conditional probability is the probability of an event occurring given that another event has occurred.

Q: What is the concept of Bayes' theorem?

A: Bayes' theorem is a formula that describes the relationship between conditional probability and prior probability.

Conclusion

In conclusion, probability is a fundamental concept in mathematics that deals with the likelihood of an event occurring. It is a measure of the chance or uncertainty associated with a particular outcome. We have answered some frequently asked questions about probability, including the different types of probability, the difference between probability and chance, and some common probability formulas.

Frequently Asked Questions

  • What is probability?
  • How is probability calculated?
  • What are the different types of probability?
  • What is the difference between probability and chance?
  • How is probability used in real-world applications?
  • What are some common probability formulas?
  • What is the concept of independent events?
  • What is the concept of dependent events?
  • What is the concept of conditional probability?
  • What is the concept of Bayes' theorem?

Answers

  • Probability is a numerical value between 0 and 1 that represents the likelihood of an event occurring.
  • Probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes.
  • The different types of probability are theoretical probability and experimental probability.
  • Probability and chance are related but distinct concepts.
  • Probability is used in many real-world applications, such as insurance, finance, medicine, and engineering.
  • Some common probability formulas include P(E) = Number of favorable outcomes / Total number of possible outcomes, P(E) = 1 - P(E'), and P(E ∪ F) = P(E) + P(F) - P(E ∩ F).
  • Independent events are events that do not affect each other.
  • Dependent events are events that affect each other.
  • Conditional probability is the probability of an event occurring given that another event has occurred.
  • Bayes' theorem is a formula that describes the relationship between conditional probability and prior probability.

Glossary

  • Probability: A numerical value between 0 and 1 that represents the likelihood of an event occurring.
  • Favorable outcomes: The number of outcomes that are in our favor.
  • Total number of possible outcomes: The total number of outcomes that are possible.
  • Event: A specific outcome or set of outcomes.
  • Independent events: Events that do not affect each other.
  • Dependent events: Events that affect each other.
  • Conditional probability: The probability of an event occurring given that another event has occurred.
  • Bayes' theorem: A formula that describes the relationship between conditional probability and prior probability.