Identifying Even Numbered Tiles

Oct 13, 2025 by windailys.com 21 views

Introduction

In probability theory, the likelihood of an event occurring is often measured by its probability. In this article, we will explore the concept of probability and apply it to a real-world scenario involving Carolyn, who randomly selects a tile from a given set. Our objective is to determine the probability that Carolyn selected a white tile or a tile with an even number.

Understanding 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 are interested in finding the probability of Carolyn selecting a white tile or a tile with an even number.

The Set of Tiles

The set of tiles shown below consists of 11 tiles with different numbers and colors.

Number	Color
2	White
2	White
3	Red
1	Red
2	White
3	Red
4	White
1	Red
4	White
1	Red
2	White

Identifying White Tiles

From the set of tiles, we can identify the white tiles as follows:

Tile 2 (White)
Tile 2 (White)
Tile 2 (White)
Tile 4 (White)
Tile 4 (White)

There are a total of 5 white tiles in the set.

Identifying Even Numbered Tiles

Next, we need to identify the tiles with even numbers. These are the tiles with numbers 2 and 4.

Tile 2 (White)
Tile 2 (White)
Tile 2 (White)
Tile 4 (White)
Tile 4 (White)
Tile 2 (White)

There are a total of 6 tiles with even numbers in the set.

Overlapping Tiles

We need to consider the tiles that are both white and have even numbers. These are the tiles with numbers 2 and 4 that are white.

Tile 2 (White)
Tile 2 (White)
Tile 2 (White)
Tile 4 (White)
Tile 4 (White)

There are a total of 5 tiles that are both white and have even numbers.

Calculating the Probability

To calculate the probability of Carolyn selecting a white tile or a tile with an even number, we need to use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

where P(A) is the probability of selecting a white tile, P(B) is the probability of selecting a tile with an even number, and P(A and B) is the probability of selecting a tile that is both white and has an even number.

Probability of Selecting a White Tile

The probability of selecting a white tile is the number of white tiles divided by the total number of tiles.

P(A) = Number of white tiles / Total number of tiles = 5 / 11

Probability of Selecting a Tile with an Even Number

The probability of selecting a tile with an even number is the number of tiles with even numbers divided by the total number of tiles.

P(B) = Number of tiles with even numbers / Total number of tiles = 6 / 11

Probability of Selecting a Tile that is Both White and has an Even Number

The probability of selecting a tile that is both white and has an even number is the number of tiles that are both white and have even numbers divided by the total number of tiles.

P(A and B) = Number of tiles that are both white and have even numbers / Total number of tiles = 5 / 11

Applying the Formula

Now that we have calculated the individual probabilities, we can apply the formula to find the probability of Carolyn selecting a white tile or a tile with an even number.

P(A or B) = P(A) + P(B) - P(A and B) = 5/11 + 6/11 - 5/11 = 6/11

Conclusion

In conclusion, the probability of Carolyn selecting a white tile or a tile with an even number is 6/11. This means that there is a 54.55% chance that Carolyn selected a white tile or a tile with an even number.

Final Answer

Introduction

In our previous article, we explored the concept of probability and applied it to a real-world scenario involving Carolyn, who randomly selects a tile from a given set. Our objective was to determine the probability that Carolyn selected a white tile or a tile with an even number. In this article, we will answer some frequently asked questions related to the topic.

Q&A

Q: What is the probability of selecting a white tile?

A: The probability of selecting a white tile is 5/11, which is approximately 0.4545 or 45.45%.

Q: What is the probability of selecting a tile with an even number?

A: The probability of selecting a tile with an even number is 6/11, which is approximately 0.5455 or 54.55%.

Q: What is the probability of selecting a tile that is both white and has an even number?

A: The probability of selecting a tile that is both white and has an even number is 5/11, which is approximately 0.4545 or 45.45%.

Q: How do you calculate the probability of two events occurring?

A: To calculate the probability of two events occurring, you can use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

where P(A) is the probability of event A occurring, P(B) is the probability of event B occurring, and P(A and B) is the probability of both events A and B occurring.

Q: What is the difference between the probability of two events occurring and the probability of two events not occurring?

A: The probability of two events occurring is the probability of both events happening together. The probability of two events not occurring is the probability of either event not happening.

Q: Can you give an example of how to use the formula to calculate the probability of two events occurring?

A: Let's say we have two events: A and B. The probability of event A occurring is 3/5, and the probability of event B occurring is 2/3. We want to find the probability of both events occurring. Using the formula, we get:

P(A and B) = P(A) * P(B) = (3/5) * (2/3) = 6/15 = 2/5

Q: What is the relationship between probability and statistics?

A: Probability and statistics are closely related fields of study. Probability deals with the likelihood of events occurring, while statistics deals with the analysis and interpretation of data. In many cases, probability is used to make predictions about future events, and statistics is used to analyze the results of those predictions.

Q: Can you give an example of how probability is used in real-life scenarios?

A: Yes, probability is used in many real-life scenarios, such as:

Insurance companies use probability to determine the likelihood of an accident occurring and to set premiums accordingly.
Financial institutions use probability to determine the likelihood of a stock or bond performing well and to make investment decisions.
Medical professionals use probability to determine the likelihood of a patient recovering from a disease and to make treatment decisions.

Conclusion

In conclusion, probability is a fundamental concept in mathematics and statistics that is used to determine the likelihood of events occurring. In this article, we answered some frequently asked questions related to the topic and provided examples of how probability is used in real-life scenarios. We hope this article has been helpful in understanding the concept of probability and its applications.