Probability of Choosing 1 Blue Marble

Oct 13, 2025 by windailys.com 56 views

Introduction

Probability is a fundamental concept in mathematics that helps us understand the likelihood of events occurring. In this article, we will explore the probability of selecting different colored marbles from a bag containing 2 blue marbles, 3 red marbles, and 5 white marbles. We will calculate the probability of choosing 1 blue marble, 1 red marble, and 1 red marble without replacement, and determine which events have a probability greater than $\frac{1}{5}$ .

The Bag of Marbles

The bag contains a total of 10 marbles, consisting of:

2 blue marbles
3 red marbles
5 white marbles

Choosing 1 Blue Marble

To calculate the probability of choosing 1 blue marble, we need to divide the number of blue marbles by the total number of marbles in the bag.

Probability of Choosing 1 Blue Marble

The probability of choosing 1 blue marble is:

P(\text{blue}) = \frac{\text{Number of blue marbles}}{\text{Total number of marbles}} = \frac{2}{10} = \frac{1}{5}

As we can see, the probability of choosing 1 blue marble is exactly $\frac{1}{5}$ , which is not greater than $\frac{1}{5}$ .

Choosing 1 Red Marble

To calculate the probability of choosing 1 red marble, we need to divide the number of red marbles by the total number of marbles in the bag.

Probability of Choosing 1 Red Marble

The probability of choosing 1 red marble is:

P(\text{red}) = \frac{\text{Number of red marbles}}{\text{Total number of marbles}} = \frac{3}{10}

Since $\frac{3}{10}$ is greater than $\frac{1}{5}$ , the probability of choosing 1 red marble is greater than $\frac{1}{5}$ .

Choosing 1 Red Marble, Not Replacing It

To calculate the probability of choosing 1 red marble without replacement, we need to consider the number of red marbles remaining in the bag after the first red marble is chosen.

Probability of Choosing 1 Red Marble, Not Replacing It

The probability of choosing 1 red marble without replacement is:

P(\text{red, no replacement}) = \frac{\text{Number of red marbles remaining}}{\text{Total number of marbles remaining}} = \frac{2}{9}

Since $\frac{2}{9}$ is less than $\frac{1}{5}$ , the probability of choosing 1 red marble without replacement is less than $\frac{1}{5}$ .

Conclusion

In conclusion, the events with a probability greater than $\frac{1}{5}$ are:

Choosing 1 red marble
Choosing 1 red marble, not replacing it, is not correct as it is less than 1/5.

However, we can select three options from the above results.

Choosing 1 red marble
Choosing 1 red marble, not replacing it, is not correct as it is less than 1/5.
Choosing 1 blue marble is not correct as it is equal to 1/5.

So, the three options are:

Choosing 1 red marble
Choosing 1 blue marble
Choosing 1 white marble
A Bag of Marbles: Exploring Probability =====================================================

Q&A: A Bag of Marbles

Q: What is the probability of choosing 1 blue marble from the bag?

A: The probability of choosing 1 blue marble is $\frac{1}{5}$ , since there are 2 blue marbles out of a total of 10 marbles in the bag.

Q: What is the probability of choosing 1 red marble from the bag?

A: The probability of choosing 1 red marble is $\frac{3}{10}$ , since there are 3 red marbles out of a total of 10 marbles in the bag.

Q: What is the probability of choosing 1 red marble without replacement from the bag?

A: The probability of choosing 1 red marble without replacement is $\frac{2}{9}$ , since there are 2 red marbles remaining out of a total of 9 marbles in the bag after the first red marble is chosen.

Q: Which events have a probability greater than $\frac{1}{5}$ ?

A: The events with a probability greater than $\frac{1}{5}$ are:

Choosing 1 red marble
Choosing 1 white marble

Q: What is the total number of marbles in the bag?

A: The total number of marbles in the bag is 10, consisting of 2 blue marbles, 3 red marbles, and 5 white marbles.

Q: What is the probability of choosing 1 white marble from the bag?

A: The probability of choosing 1 white marble is $\frac{5}{10}$ , since there are 5 white marbles out of a total of 10 marbles in the bag.

Q: Can we calculate the probability of choosing 2 red marbles without replacement from the bag?

A: Yes, we can calculate the probability of choosing 2 red marbles without replacement from the bag. The probability of choosing 2 red marbles without replacement is:

P(\text{2 red, no replacement}) = \frac{\text{Number of red marbles remaining}}{\text{Total number of marbles remaining}} = \frac{1}{8}

Q: Can we calculate the probability of choosing 2 blue marbles without replacement from the bag?

A: Yes, we can calculate the probability of choosing 2 blue marbles without replacement from the bag. The probability of choosing 2 blue marbles without replacement is:

P(\text{2 blue, no replacement}) = \frac{\text{Number of blue marbles remaining}}{\text{Total number of marbles remaining}} = \frac{1}{9}

Q: Can we calculate the probability of choosing 2 white marbles without replacement from the bag?

A: Yes, we can calculate the probability of choosing 2 white marbles without replacement from the bag. The probability of choosing 2 white marbles without replacement is:

P(\text{2 white, no replacement}) = \frac{\text{Number of white marbles remaining}}{\text{Total number of marbles remaining}} = \frac{4}{9}

Conclusion

In conclusion, we have explored the probability of choosing different colored marbles from a bag containing 2 blue marbles, 3 red marbles, and 5 white marbles. We have calculated the probability of choosing 1 blue marble, 1 red marble, and 1 red marble without replacement, and determined which events have a probability greater than $\frac{1}{5}$ . We have also answered several questions related to the bag of marbles and its contents.