A Bag Contains Eleven Equally Sized Marbles, Which Are Numbered.What Is The Probability That A Marble Chosen At Random Is Shaded Or Is Labeled With A Multiple Of 3?A. { \frac{2}{11}$}$B. { \frac{3}{11}$}$C.

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A Bag of Marbles: Understanding Probability

Probability is a fundamental concept in mathematics that deals with the likelihood of an event occurring. In this article, we will explore the concept of probability by analyzing a bag containing eleven equally sized marbles, each numbered. We will determine the probability that a marble chosen at random is either shaded or labeled with a multiple of 3.

Let's assume that the bag contains eleven marbles, each numbered from 1 to 11. Out of these eleven marbles, some are shaded, and some are labeled with a multiple of 3. We need to find the probability that a marble chosen at random is either shaded or labeled with a multiple of 3.

Defining the Sample Space

The sample space is the set of all possible outcomes. In this case, the sample space consists of the eleven marbles in the bag. We can represent the sample space as S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}.

Defining the Event

The event is the set of outcomes that we are interested in. In this case, the event is the set of marbles that are either shaded or labeled with a multiple of 3. We can represent the event as E = {3, 6, 9}.

Calculating the Probability

The probability of an event is defined as the number of favorable outcomes divided by the total number of possible outcomes. In this case, the number of favorable outcomes is the number of marbles that are either shaded or labeled with a multiple of 3, which is 4 (3, 6, 9, and 1 additional marble). The total number of possible outcomes is the total number of marbles in the bag, which is 11.

Using the Formula

We can use the formula for probability to calculate the probability of the event:

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

P(E) = 4 / 11

Simplifying the Fraction

We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 1.

P(E) = 4 / 11

In conclusion, the probability that a marble chosen at random from a bag containing eleven equally sized marbles is either shaded or labeled with a multiple of 3 is 4/11.

  • The probability of an event is always between 0 and 1.
  • The probability of an event is 0 if the event is impossible, and it is 1 if the event is certain.
  • The probability of an event can be calculated using the formula P(E) = Number of favorable outcomes / Total number of possible outcomes.

Probability has numerous real-world applications in fields such as finance, insurance, and medicine. For example, probability is used in:

  • Finance: To calculate the likelihood of a stock price increasing or decreasing.
  • Insurance: To determine the likelihood of an accident occurring.
  • Medicine: To calculate the likelihood of a patient recovering from a disease.

In conclusion, probability is a fundamental concept in mathematics that deals with the likelihood of an event occurring. By understanding probability, we can make informed decisions in various aspects of life. The probability that a marble chosen at random from a bag containing eleven equally sized marbles is either shaded or labeled with a multiple of 3 is 4/11.

  • Probability: The likelihood of an event occurring.
  • Sample Space: The set of all possible outcomes.
  • Event: The set of outcomes that we are interested in.
  • Favorable Outcomes: The number of outcomes that are favorable to the event.
  • Total Number of Possible Outcomes: The total number of outcomes in the sample space.
    A Bag of Marbles: Understanding Probability - Q&A

In our previous article, we explored the concept of probability by analyzing a bag containing eleven equally sized marbles, each numbered. We determined the probability that a marble chosen at random is either shaded or labeled with a multiple of 3. In this article, we will answer some frequently asked questions related to the topic.

Q: What is the probability that a marble chosen at random is shaded?

A: To calculate the probability that a marble chosen at random is shaded, we need to know the number of shaded marbles and the total number of marbles in the bag. Let's assume that there are 3 shaded marbles in the bag. The probability that a marble chosen at random is shaded is:

P(shaded) = Number of shaded marbles / Total number of marbles = 3 / 11

Q: What is the probability that a marble chosen at random is labeled with a multiple of 3?

A: To calculate the probability that a marble chosen at random is labeled with a multiple of 3, we need to know the number of marbles labeled with a multiple of 3 and the total number of marbles in the bag. Let's assume that there are 3 marbles labeled with a multiple of 3 in the bag. The probability that a marble chosen at random is labeled with a multiple of 3 is:

P(multiple of 3) = Number of marbles labeled with a multiple of 3 / Total number of marbles = 3 / 11

Q: What is the probability that a marble chosen at random is either shaded or labeled with a multiple of 3?

A: We already calculated this probability in our previous article. The probability that a marble chosen at random is either shaded or labeled with a multiple of 3 is:

P(shaded or multiple of 3) = 4 / 11

Q: Can we use the formula for probability to calculate the probability of an event that has multiple outcomes?

A: Yes, we can use the formula for probability to calculate the probability of an event that has multiple outcomes. However, we need to make sure that the outcomes are mutually exclusive, meaning that they cannot occur at the same time.

Q: What is the difference between the probability of an event and the probability of the complement of an event?

A: The probability of an event is the likelihood of the event occurring, while the probability of the complement of an event is the likelihood of the event not occurring. For example, if the probability of an event is 0.5, the probability of the complement of the event is 0.5.

Q: Can we use the formula for probability to calculate the probability of an event that has a dependent outcome?

A: No, we cannot use the formula for probability to calculate the probability of an event that has a dependent outcome. Dependent outcomes are outcomes that are not independent of each other, meaning that the occurrence of one outcome affects the probability of the other outcome.

In conclusion, probability is a fundamental concept in mathematics that deals with the likelihood of an event occurring. By understanding probability, we can make informed decisions in various aspects of life. We hope that this article has helped to answer some of the frequently asked questions related to the topic.

  • The probability of an event is always between 0 and 1.
  • The probability of an event is 0 if the event is impossible, and it is 1 if the event is certain.
  • The probability of an event can be calculated using the formula P(E) = Number of favorable outcomes / Total number of possible outcomes.

Probability has numerous real-world applications in fields such as finance, insurance, and medicine. For example, probability is used in:

  • Finance: To calculate the likelihood of a stock price increasing or decreasing.
  • Insurance: To determine the likelihood of an accident occurring.
  • Medicine: To calculate the likelihood of a patient recovering from a disease.

In conclusion, probability is a fundamental concept in mathematics that deals with the likelihood of an event occurring. By understanding probability, we can make informed decisions in various aspects of life. We hope that this article has helped to answer some of the frequently asked questions related to the topic.

  • Probability: The likelihood of an event occurring.
  • Sample Space: The set of all possible outcomes.
  • Event: The set of outcomes that we are interested in.
  • Favorable Outcomes: The number of outcomes that are favorable to the event.
  • Total Number of Possible Outcomes: The total number of outcomes in the sample space.