A Bag Contains 5 Red, 4 Green, And 3 Blue Marbles. What Is The Probability Of Randomly Selecting A Blue Marble, Replacing It In The Bag, And Then Randomly Selecting A Red Marble?A. $\frac{1}{48}$B. $\frac{1}{12}$C.

Feb 27, 2025 by ADMIN 219 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, replacing it in the bag, and then randomly selecting a red marble from a bag containing 5 red, 4 green, and 3 blue marbles.

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 want to find the probability of selecting a blue marble and then a red marble.

Step 1: Selecting a Blue Marble

To find 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(\text{blue}) = \frac{3}{12} = \frac{1}{4}

Step 2: Replacing the Blue Marble

Since we are replacing the blue marble in the bag, the total number of marbles remains the same. The probability of selecting a blue marble again is still:

P(\text{blue}) = \frac{1}{4}

Step 3: Selecting a Red Marble

Now, we need 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(\text{red}) = \frac{5}{12}

Finding the Overall Probability

To find the overall probability of selecting a blue marble and then a red marble, we need to multiply the probabilities of each step.

P(\text{blue and red}) = P(\text{blue}) \times P(\text{red}) = \frac{1}{4} \times \frac{5}{12} = \frac{5}{48}

In conclusion, the probability of randomly selecting a blue marble, replacing it in the bag, and then randomly selecting a red marble from a bag containing 5 red, 4 green, and 3 blue marbles is $\frac{5}{48}$ .

The correct answer is:

\frac{5}{48}

However, since the answer choices are not in the same format, we can simplify the fraction to:

\frac{5}{48} = \frac{1}{9.6} \approx \frac{1}{10}

So, the closest answer choice would be:

\frac{1}{12}

But this is not the exact answer. The correct answer is not among the options provided.
Probability of Selecting a Blue and Then a Red Marble: Q&A

In our previous article, we explored the concept of probability and calculated the probability of randomly selecting a blue marble, replacing it in the bag, and then randomly selecting 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 this topic.

Q: What is the probability of selecting a blue marble first and then a red marble?

A: The probability of selecting a blue marble first is $\frac{1}{4}$ , and the probability of selecting a red marble is $\frac{5}{12}$ . To find the overall probability, we multiply these two probabilities:

P(\text{blue and red}) = P(\text{blue}) \times P(\text{red}) = \frac{1}{4} \times \frac{5}{12} = \frac{5}{48}

Q: What if we don't replace the blue marble?

A: If we don't replace the blue marble, the total number of marbles decreases by 1. So, the probability of selecting a red marble is:

P(\text{red}) = \frac{5}{11}

To find the overall probability, we multiply the probabilities of each step:

P(\text{blue and red}) = P(\text{blue}) \times P(\text{red}) = \frac{1}{4} \times \frac{5}{11} = \frac{5}{44}

Q: What if we have a different number of marbles?

A: The probability of selecting a blue marble and then a red marble depends on the number of marbles in the bag. If we have a different number of marbles, we need to recalculate the probabilities.

For example, if we have 3 blue marbles and 5 red marbles, the probability of selecting a blue marble is:

P(\text{blue}) = \frac{3}{8}

And the probability of selecting a red marble is:

P(\text{red}) = \frac{5}{8}

To find the overall probability, we multiply these two probabilities:

P(\text{blue and red}) = P(\text{blue}) \times P(\text{red}) = \frac{3}{8} \times \frac{5}{8} = \frac{15}{64}

Q: Can we use a formula to calculate the probability?

A: Yes, we can use a formula to calculate the probability. The formula is:

P(\text{blue and red}) = P(\text{blue}) \times P(\text{red})

Where $P(\text{blue})$ is the probability of selecting a blue marble and $P(\text{red})$ is the probability of selecting a red marble.

Q: What is the probability of selecting a red marble first and then a blue marble?

A: The probability of selecting a red marble first is $\frac{5}{12}$ , and the probability of selecting a blue marble is $\frac{3}{12}$ . To find the overall probability, we multiply these two probabilities:

P(\text{red and blue}) = P(\text{red}) \times P(\text{blue}) = \frac{5}{12} \times \frac{3}{12} = \frac{15}{144}