Explanation:

To determine the probability that one ball is red and the other is blue, you can follow these steps:

- Calculate the total number of ways to draw two balls from the bag:

$$

\text{Total ways} = \binom{13}{2} = 78

$$

This is because there are 13 balls in total (8 red + 5 blue).

- Calculate the number of favorable ways to draw one red and one blue ball:

- Ways to choose 1 red ball from 8 red balls:

$$

\binom{8}{1} = 8

$$

- Ways to choose 1 blue ball from 5 blue balls:

$$

\binom{5}{1} = 5

$$

- Total favorable ways:

$$

8 \times 5 = 40

$$

- Probability of drawing one red and one blue ball:

$$

\frac{40}{78} = \frac{20}{39}

$$

- Option 1, 20/39, matches the calculated probability.

Option 1: 20/39

- Correct calculation based on combinatorial mathematics.

Option 2: 10/29

- Not matching with probability calculation.

Option 3: 25/39

- Incorrect, not aligned with outcomes.

Option 4: 1/13

- Significantly off.

Option 5: None of the Above

- Not applicable as Option 1 is correct.