A jar contains 5 red marbles, 2 white marbles, and 3 blue marbles. Two marbles are randomly selected from the jar with replacement. Find the following probabilities. Leave your answer as a reduced fraction.
A red marble and then a blue marble is randomly selected.

A white marble and then a red marble is randomly selected.

We can solve this using basic probability rules. Since the marbles are drawn with replacement, the probability for each draw remains unchanged.

### Total Marbles in the Jar:
The jar contains:
- 5 red marbles
- 2 white marbles
- 3 blue marbles

So, the total number of marbles is:
\[
5 + 2 + 3 = 10 \text{ marbles}.
\]

#### 1. **Probability of selecting a red marble and then a blue marble:**

The probability of selecting a red marble on the first draw:
\[
P(\text{Red}) = \frac{5}{10} = \frac{1}{2}.
\]

The probability of selecting a blue marble on the second draw (since the total number of marbles stays the same due to replacement):
\[
P(\text{Blue}) = \frac{3}{10}.
\]

Now, using the multiplication rule for independent events, the probability of selecting a red marble followed by a blue marble is:
\[
P(\text{Red and Blue}) = P(\text{Red}) \times P(\text{Blue}) = \frac{1}{2} \times \frac{3}{10} = \frac{3}{20}.
\]

#### 2. **Probability of selecting a white marble and then a red marble:**

The probability of selecting a white marble on the first draw:
\[
P(\text{White}) = \frac{2}{10} = \frac{1}{5}.
\]

The probability of selecting a red marble on the second draw:
\[
P(\text{Red}) = \frac{5}{10} = \frac{1}{2}.
\]

Now, the probability of selecting a white marble followed by a red marble is:
\[
P(\text{White and Red}) = P(\text{White}) \times P(\text{Red}) = \frac{1}{5} \times \frac{1}{2} = \frac{1}{10}.
\]

### Final Answers:
1. The probability of selecting a red marble and then a blue marble is \( \frac{3}{20} \).
2. The probability of selecting a white marble and then a red marble is \( \frac{1}{10} \).

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the probability of selecting two red marbles in a row?
2. What is the probability of selecting a blue marble and then a white marble?
3. What is the probability of selecting two white marbles in a row?
4. How does the probability change if marbles are drawn without replacement?
5. What is the probability of selecting two marbles of the same color?

**Tip**: When events are independent, you can find the combined probability by multiplying the individual probabilities of each event.

A jar contains 5 red marbles, 2 white marbles, and 3 blue marbles. Two marbles are randomly selected from the jar with replacement. Find the following probabilities: A red marble and then a blue marble is randomly selected. A white marble and then a red marble is randomly selected.

Learn how to calculate the probability of selecting a red marble followed by a blue marble, and a white marble followed by a red marble from a jar containing 5 red, 2 white, and 3 blue marbles, with replacement. This step-by-step guide covers the use of independent events and the multiplication rule. Suitable for students in Grades 6-8.

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