Probability of Selecting a Blue and Then a Red Marble

Oct 13, 2025 by windailys.com 102 views

Probability of Selecting a Blue and Then a Red Marble

In this article, we will explore the concept of probability and how it applies to a real-world scenario. We will calculate the probability of randomly selecting a blue marble from a bag containing 5 red, 4 green, and 3 blue marbles, replacing it in the bag, and then randomly selecting a red marble.

Probability is a measure of the likelihood of an event occurring. It is usually expressed as a number 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 of selecting a blue marble and then a red marble.

To calculate the probability of selecting a blue marble, we need to divide the number of blue marbles by the total number of marbles in the bag.

There are 3 blue marbles and a total of 12 marbles (5 red + 4 green + 3 blue). So, the probability of selecting a blue marble is:

P(blue) = Number of blue marbles / Total number of marbles P(blue) = 3/12 = 1/4

Now, let's assume that we replace the blue marble in the bag. This means that the total number of marbles remains the same, but the number of blue marbles is now 3 again.

Next, we want to find the probability of selecting a red marble. There are 5 red marbles and a total of 12 marbles. So, the probability of selecting a red marble is:

P(red) = Number of red marbles / Total number of marbles P(red) = 5/12

Since we are replacing the blue marble, the probability of selecting a red marble remains the same.

Now, we want to find the probability of both events occurring: selecting a blue marble and then a red marble. To do this, we need to multiply the probabilities of each event.

P(blue and red) = P(blue) x P(red) P(blue and red) = 1/4 x 5/12 P(blue and red) = 5/48

Therefore, the probability of randomly selecting a blue marble, replacing it in the bag, and then randomly selecting a red marble is 5/48.

In this article, we calculated the probability of selecting a blue marble and then a red marble from a bag containing 5 red, 4 green, and 3 blue marbles. We found that the probability of both events occurring is 5/48.

What is the probability of selecting a blue marble?
The probability of selecting a blue marble is 1/4.
What is the probability of selecting a red marble?
The probability of selecting a red marble is 5/12.
What is the probability of both events occurring?
The probability of both events occurring is 5/48.

[1] Probability Theory, by E.T. Jaynes
[2] Statistics, by W.H. Kruskal and J.M. Tanur

Probability: A measure of the likelihood of an event occurring.
Event: A specific outcome or occurrence.
Independent events: Events that do not affect each other's probability.
Dependent events: Events that affect each other's probability.

Probability theory
Statistics
Random variables
Conditional probability

Probability Theory, by E.T. Jaynes
Statistics, by W.H. Kruskal and J.M. Tanur
Random Variables, by J.L. Doob

In conclusion, the probability of randomly selecting a blue marble, replacing it in the bag, and then randomly selecting a red marble is 5/48. This article has provided a step-by-step guide to calculating the probability of two independent events occurring.
Probability Q&A: Frequently Asked Questions

In our previous article, we explored the concept of probability and calculated the probability of randomly selecting a blue marble and then a red marble from a bag containing 5 red, 4 green, and 3 blue marbles. In this article, we will answer some frequently asked questions related to probability.

Q: What is probability?

A: Probability is a measure of the likelihood of an event occurring. It is usually expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

Q: What is the difference between probability and chance?

A: Probability is a mathematical concept that measures 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 do I calculate the probability of an event?

A: To calculate the probability of an event, you need to divide the number of favorable outcomes by the total number of possible outcomes.

Q: What is the formula for probability?

A: The formula for probability is:

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

Q: What is the difference between independent and dependent events?

A: Independent events are events that do not affect each other's probability, while dependent events are events that affect each other's probability.

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

A: To calculate the probability of two independent events occurring, you need to multiply the probabilities of each event.

Q: What is the formula for the probability of two independent events?

A: The formula for the probability of two independent events is:

P(event 1 and event 2) = P(event 1) x P(event 2)

Q: What is the difference between conditional probability and unconditional probability?

A: Conditional probability is the probability of an event occurring given that another event has occurred, while unconditional probability is the probability of an event occurring without any conditions.

Q: How do I calculate the conditional probability of an event?

A: To calculate the conditional probability of an event, you need to divide the number of favorable outcomes by the total number of possible outcomes, given that the other event has occurred.

Q: What is the formula for conditional probability?

A: The formula for conditional probability is:

P(event | event 1) = P(event and event 1) / P(event 1)

Q: What is the difference between probability and statistics?

A: Probability is a mathematical concept that measures the likelihood of an event occurring, while statistics is the study of the collection, analysis, interpretation, presentation, and organization of data.

Q: How do I apply probability in real-life situations?

A: Probability is used in many real-life situations, such as insurance, finance, medicine, and engineering. It helps us make informed decisions by quantifying the likelihood of different outcomes.

In conclusion, probability is a fundamental concept in mathematics that measures the likelihood of an event occurring. By understanding probability, we can make informed decisions and quantify the uncertainty of different outcomes. This article has provided a comprehensive guide to frequently asked questions related to probability.

What is probability?
What is the difference between probability and chance?
How do I calculate the probability of an event?
What is the formula for probability?
What is the difference between independent and dependent events?
How do I calculate the probability of two independent events?
What is the formula for the probability of two independent events?
What is the difference between conditional probability and unconditional probability?
How do I calculate the conditional probability of an event?
What is the formula for conditional probability?
What is the difference between probability and statistics?
How do I apply probability in real-life situations?

[1] Probability Theory, by E.T. Jaynes
[2] Statistics, by W.H. Kruskal and J.M. Tanur
[3] Random Variables, by J.L. Doob

Probability: A measure of the likelihood of an event occurring.
Event: A specific outcome or occurrence.
Independent events: Events that do not affect each other's probability.
Dependent events: Events that affect each other's probability.
Conditional probability: The probability of an event occurring given that another event has occurred.
Unconditional probability: The probability of an event occurring without any conditions.

Probability theory
Statistics
Random variables
Conditional probability

Probability Theory, by E.T. Jaynes
Statistics, by W.H. Kruskal and J.M. Tanur
Random Variables, by J.L. Doob