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.